Free entry in the Indian automobile industry: a calibration model

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Free entry in the Indianautomobile industry: acalibration modelPaul E. Jensen a & Kala Krishna ba Department of Economics and InternationalBusiness , Drexel University , USAb Department of Economics , Pennsylvania StateUniversity , USAPublished online: 28 Sep 2006.

To cite this article: Paul E. Jensen & Kala Krishna (1999) Free entry in the Indianautomobile industry: a calibration model, The Journal of International Trade &Economic Development: An International and Comparative Review, 8:4, 437-455,DOI: 10.1080/09638199900000026

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J. Int. Trade & Econornic Development 8:4 437-455

Free entry in the Indian automobile industry: a calibration model Paul E. Jensent and Kala Krishnas tDrexel University, Department of Economics and International Business, USA; $Pennsylvania State University, Department of Economics, USA

Abstract

We examine the implications of free entry in the Indian automobile industry in a model that is calibrated to the Indian market using price, cost and production data from 1993 and 1994. In particular, we consider the effect that free entry has on prices, production levels and welfare. We have two main findings. First, that despite the experiences of other countries, free entry is a desirable policy in this market. Second, that the excise tax of 40 per cent levied on automobiles does not seem to have a major adverse impact on welfare.

Keywords

Entry, calibration, industrial policy, product differentiation, automobiles, India

1. INTRODUCTION

The industrial sector in India has traditionally seen substantial government regulation. Most durable consumer goods were viewed as luxury goods and consumption was discouraged by high excise taxes and prohibitive tariffs. In addition, production - at all but the small scale - was controlled and limited by government-issued production licences. In recent years there has been a movement towards liberalization. This has typically taken the form of reduced excise taxes and free entry for producers. Recently, the Indian automobile industry was 'reformed' as excise taxes were reduced and the industry was de-licensed. Implicit in this policy seems to be the assumption that a movement towards free entry is necessarily welfare improving. It is not at all clear that this assumption is true in general.

The current paper is the second in a two paper series that examines the welfare consequences of industrial policy in imperfectly competitive industries in open economies. The first paper examined how various characteristics of the industry affect changes in welfare due to liberalization of entry policy.' Spence (1976a) and Mankiw and Whinston (1986) show that in a closed

Address for Correspondence Paul Jensen, Department of Economics, Drexel University, 503 Matherson Hall, Philadelphia, PA 191 04, USA.

The Journal of International Trade & Economic Development I S S N 0963-8199 O 1999 Taylor & Francis Ltd

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438 The Journal of International Trade & Economic Development

economy free entry leads to an excessive entry when goods are homogeneous. With product differentiation this need not be the case. There are two opposing effects of entry which they refer to as the 'business stealing effect' and the 'variety effect'. The business stealing effect arises because markets are imperfectly competitive and thus firms are earning profits. New firms reduce the profits of all existing firms. As entering firms do not consider this negative externality of their actions, entry is excessive. When products are differentiated, variety is valued for its own sake. Since entering firms cannot capture all the consumer surplus gains the variety effect tends to result in insufficient entry.

In our first paper, we look at the implications of entry with domestic and foreign firms. The composition of firms is important because it determines the extent to which the profit stealing effect reduces home country welfare. If all firms are domestic then the home country feels the full effect of profit stealing when new firms enter. However, if some of the firms in the market are foreign then the home country is only subject to a portion of the lost profits. Therefore, a movement towards free entry is more likely to be welfare improving if there are foreign firms present in the market.

This paper models the Indian automobile industry and examines the welfare consequences of policy reform. We derive results from a calibrated partial equilibrium model. There is a sizeable literature on calibrated models with imperfect competition in a world with product differentiation and increasing returns. Brown et al. (1995) and Lopez-de-Silanes et al. (1994) focus on the likely effects of NAFTA in such a CGE model, while Harrison et al. (1997) look at the Uruguay Round.

Closest to our work is that of de Melo and Tarr (1992) who examine the effects of US trade policy in automobiles as well as other industries. Among other things, they examine the reasons for differences in the results of partial and general equilibrium models. There are many reasons for this. Partial equilibrium models assume that what happens in this sector has no impact on other sectors. This is not likely to be a good approximation when sectors are closely related either vertically, as with steel and automobiles, or horizontally, as with cars and vans. More subtly, they argue (de Melo and Tam, 1992: 8) that partial equilibrium models tend to give larger effects of trade restrictions than do general equilibrium models as the former neglect trade balance. Thus, for given terms of trade, making a quota increasingly restrictive in one sector, which reduces excess demand and import value in that sector, must be raising excess demand in other sectors.

Terms of trade effects can also be important. A quota that improves the terms of trade has an add~tional welfare gain. Both of these tend to make partial equilibrium estimates of costs of protection higher than CGE estimates. De Melo and Tarr (1992: 192), in contrast, find their estimates exceed those under partial equilibrium and suggest that this is due to their use of larger quota premia, their assumption of lower terms of trade effects than in standard

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Free entry in the Indian automobile industry 439

models (which make the Armington Assumption), and a greater extent of increasing returns.

Our partial equilibrium approach enables us to evaluate government policies with the minimal data available. The paper builds on the work of Dixit (1988) and Krishna et al. (1989). Both of these papers examined optimal tax and tariff policies for the US automobile industry in the context of a partial equilibrium calibration model but neither examines free entry. Rodrik (1988) does address the issue of free entry in a calibration model but he does not consider product differentiation as we do. This paper does not consider optimal trade policies, as imports are prohibitively taxed in India and so are assumed to be banned, but rather focuses on the effects of free entry and domestic tax policies.

2. THE MODEL

The model to be employed is an augmented version of one developed by Krishna et al. (1989). It is augmented on the cost side by allowing fixed and variable costs to change with the scale of production and on the behavioural side by allowing for free entry of firms. Let the number of home and foreign firms be denoted by Nand M respectively. Utility is defined by

U(S) = BSa + no (1) where n , is a numeraire good, B is a scale parameter, a is a measure of the price elasticity of demand for S, and the 'aggregate' good S is given by

With this form, p parameterizes the substitutability between home goods x and foreign goods y. The substitutability of goods within countries is measured by p, and p,. S can be interpreted as the service derived by the representative consumer from the varieties of foreign and domestic goods. The consumer purchases the individual goods x' and yi and produces the aggregate goods X and Y using a household production function. The household production functions are given by

These aggregate foods are then used to produce the services S. Since consumers create X, Y and S using constant returns to scale household production

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functions, price is equal to the cost of production for these goods. Price is greater than marginal cost for the individual goods xi and y' as these firms have market power.

The cost functions for the aggregate goods X and Y can be derived from the constant elasticity of substitution (CES) form of the production functions. These functions are:

where vi and wi correspond to the consumerprices of home and foreign goods which are inclusive of an excise tax, and where r, = p.J(p,,. - 1 ) and r,, = p J(p, - 1 ) .

The cost function for the production of S can be obtained fromthe CES production function and is given by:

where r = pl(p - 1 ) . Equating the marginal utility of S with the marginal cost, C, and inverting

gives the demand for services:

The cost functions for X and Y can be differentiated to yield the unit input requirements of xi and y' for the aggregate goods. Similarly, we can differ- entiate the cost function for services to solve for the unit input requirements of X and Y in the production of S. With all the unit input requirements and the demand for service, we can impose symmetry within each country and solve for the demands for each individual firm.? The individual demands for home and foreign are: D

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Summing the individual demand equations over the N home firms and the M foreign firms gives aggregate demand equations for the two sectors:

From the individual demand equations one can derive all the possible own and cross-elasticities of demand. If we define @ = (p/q)', and use i and j to denote firms and x and y to denote countries then we can write the within country demand elasticities as:

E i i (x , .) = - - a' - v i = - [[1 - r x ) ( N - 1 ) + 1 - r+ E$ avi xi N I + $ 1

Similarly we can express the between country demand elasticities as:

The demand elasticity for services equals3:

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442 The Journal o f lnternational Trade & Economic Developmerit

Now we can consider the firms' profit functions and first-order conditions. Profits for the typical home firm are:

where v' is the producer's price net of the excise tax, AVC is the average variable cost, and F is a fixed cost.4 The profit function for the foreign firms is analogous. Profit maximization yields the following first-order condition for the home firms:

where d., is marginal cost, t is the ad valorem tax, and y, is a conjectural variations parameter.

The foreign firms' first-order condition is:

where y, is the conjectural variations parameter for the foreign firms. These reaction functions can be solved for equilibrium prices v and w. Once the equilibrium prices are known then social welfare, the sum of home firm profits, consumer surplus, and tax revenue can be evaluated.

The two demand equations, (11) and (12), and the two first-order conditions, equations (21) and (22), provide a four-equation system with seven unknowns: .)I,, y,,, a, p, r, r., and r,,. There are numerous ways to calibrate the model but the availability of' existing estimates of several of the parameters makes some approaches more feasible than others. We choose, for reasons discussed later, to take existing estimates of a, r and r,.. With these parameters and data for v , w, t , M and N, equations (1 1 ) and (12) can be solved for P and r,. Now everything in the two first-order conditions is known except the conjectural variation parameters. Thus, equations (2 1 ) and (22) can be solved for yI and Y,. which completes the calibration procedure.

We also consider the free entry case. Free entry implies that home and foreign firms earn zero profits and thus:

These additional equations allow us to endogenize the number of home and foreign firms.

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3. THE DATA

Data on Indian automobile production and prices is summarized in Tables A1 and A2 of Appendix A. The production data are from ACMA in India and the data on prices were obtained from the Association of Indian Automobile Manufacturers. India's import tariffs on completed automobiles are prohibitive and thus all cars in India are 'produced' domestically. The cars we refer to as being domestic are those models that are built by Indian firms using Indian technology. These are primarily the models that have been around for several decades. The foreign car sector is composed of those models that are produced by foreign firms who have formed joint ventures with Indian firms. These collaborations have become much more common in India since the government began to regard access to foreign technology more favourably in the early 1980s.

For computational simplicity we use the production data in Appendix A to calculate Herfindahl numbers-equivalent for both the home and foreign sectors as the model is not tractable without imposing symmetry on the firms within each country. Thus, the observed market shares for the domestic and foreign sectors suggest that the appropriate numbers of symmetric firms, home and foreign, are: N = 3 and M = 2 respectively. This is, of course, just an approximation as the Herfindahl numbers-equivalent pertains to homogeneous goods markets. There are two alternatives to our approach. One would be simply to use the actual number of firms that would give us a total of 6 or 7 f m s . This is clearly the upper bound as the numbers-equivalent predicts fewer than the actual number of firms if the actual firms are not perfectly symmetric. Given the asymmetry of the Indian firms we should clearly expect the total number of firms to be less than 7. The second alternative is to group the home and foreign firms together and calculate the overall numbers- equivalent. This is not appealing because it forces the home and foreign firms to be identical. In Appendix D.we show that the last approach always produces a total number of firms that is less than the total number obtained by first separating the two groups and calculating the numbers-equivalent for each sector as we have done. Thus, of the three possible approaches, ours is the median case. In addition, it seems to be the approach that is most consistent with the structure of our model. Regardless, our sensitivity analysis suggests that our basic results are independent of the method selected.

Summing the quantities and taking weighted averages of the prices yields the following quantity and price data for the calibration procedure: Q, = 82 743, v = 195 815, Q, = 161 086, and w =I66 092. These prices are retail prices exclusive of the 40 per cent excise tax that is paid by consumers for all cars purchased in India. -

Data on costs are very difficult to obtain and thus a more circuitous- approach is required. What complicates the issue is that it is probably reasonable to believe that costs vary with the scale of production. A large plant will

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obviously require larger fixed costs but will probably also yield lower average variable costs as resources become more specialized. To capture these ideas we need to develop fixed and variable cost functions. The general forms of the average variable cost (AVC) function and the average fixed cost (AFC) function we use are:

a,. AVC = -

qh '.

af AFC = - qb'

(26)

where a and b are parameters and q is the quantity produced. The derivation of these cost functions is described in Appendix B.

4. CALIBRATION PROCEDURE

Dixit (1988) cites estimates of the total market demand elasticity and the elasticity of substitution between US and Japanese cars. Dixit considers a range of values for these parameters that are centred around the cited estimates. Dixit's range for E is 0.75 to 1.5 and the range for o is 1.5 to 3. Therefore, we follow Dixit (1988) and Krishna et al. (1989) and use these ranges as a guide to selecting our parameter values. Clearly the Indian auto market is different from the US and Japanese markets and thus one would not expect demand elasticities and substitution parameters to be identical across these markets. We choose o and o,, on the high end as most cars in India are similar in that they tend to be small in size and power. Our sensitivity analysis looks at the effect of choice of parameters.

For our base case we set E = I . l , o= 3 and o,.= 3.2. The calibration results for the base case are shown in Table C1 of ~ ~ ~ e n d i x C. We first note that the solution q, = 5.8 is reasonable in that q, is greater than o which confirms our belief that goods within a country are closer substitutes than goods between countries. This result also suggests that Indian automobiles are less differentiated than the foreign cars as q, is larger than o,,. This notion is also seen in the demand elasticities, as the own and within country demand elasticities for the home firms, e"(x,x) and E'i(x,x), are larger than the corresponding elasticities of the foreign sector.

The conjectural variation parameters give us an indication of how competitively the firms behave in the two sectors. A value of zero implies that behaviour is equivalent to Bertrand competition. If y is positive it suggests that f m s are more collusive than Bertrand as a price increase by one firm tends to result in price increases by other firms. Finally, if y is negative it suggests that firms behave more competitively than Bertrand oligopolists. The calibration results indicate that the home sector is less competitive than Bertrand and the foreign sector is more competitive than Bertrand competi t i~n.~ In addition, we

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see that the foreign firms behave more competitively than the home firms as y, is less than y,.

5. SIMULATION RESULTS

Using our open economy model of differentiated products, which is calibrated to the Indian market, we can now simulate the effects of a free entry policy. The results for the base case simulation are presented in Table C2. Our simulations suggest that free entry will result in substantial structural changes in the auto industry. Most notable is the number of foreign f m s entering the industry, as our base case simulation has the number of foreign firms increasing from 2 to 18.3. However, despite the tremendous increase in the number of firms there is only a 47 per cent increase in total foreign car production as each foreign firm only produces 12 900 cars as opposed to 80 543 in the status quo case. Only 1.8 home firms enter the industry but, as is the case of the foreign firms, free entry greatly reduces the scale of production of the home firms. The net result is that total home sector production falls from 82 743 to 19 204.

The large discrepancy in the amount of entry in the two sectors is explained by two factors. First, our method for calibrating the model imposes identical mark-ups for both sectors in the status quo case. As a result, foreign firms earn higher profits because they produce larger quantities. Second, the calibration also implies that the goods in the home sector are closer substitutes than the goods in the foreign sector. Since the consumer is willing to pay more for the greater variety found in the foreign sector, profits will fall more slowly in this sector than in the home sector as firms begin to enter. These effects reinforce each other and result in a relatively large number of foreign firms.

The drastic changes in the scale of production are a reason for concern regarding a free entry policy as firms are not able to take advantage of the returns to scale typically found in the automobile industry. The significance of the small-scale production is'reflected clearly in the fact that free entry results in an 8 per cent increase in car prices despite a 4.5 per cent increase in the total market supply! One does not normally associate rising prices with an increasing number of firms and increasing supply but, as we have already mentioned, this is in part due to the rising average costs that result from small production runs. The other factor that is driving prices up is the 'variety effect' associated with the CES utility function. As a wider variety of cars becomes available to consumers they consume less of each variety and thus the marginal utility of consumption rises, thus raising the consumer's willingness to pay for any particular variety.

It is interesting to note that since our results are based on data from 1993- 1994 we can examine more recent developments in the Indian auto industry in an attempt to verify our model's predictions. Our base case suggested that free entry would lead to approximately 18 new firms entering the industry. With six new firms, Daewoo, GM, Honda, Ind Auto, Mercedes Benz, and PAL peugeot6

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entering the industry by 1999 it is clear that our model's prediction in terms of the number of entrants is a bit high. Our model predicts only modest gains in total capacity whereas most projections have sales growing to half a million by 2000. The fact that our model comes up short in terms of capacity is perhaps not too surprising given the CES form we have assumed. In terms of utility, and hence demand, the CES form tends to put a premium on variety while placing a smaller weight on overall quantity increases. Moreover, in models with free entry, entry is likely to affect the behavioural parameters. If more entry enhances competition, then a model where entry does not affect behaviour, as in our case, will tend to overstate the extent of entry. This is likely to be why our entry numbers are larger than those that actually occurred.

Lastly we consider the welfare implications of the free entry policy. Wel- fare is simply the sum of consumer surplus, home firms7 profits, and tax revenues. Ex ante, it is not clear what effect free entry will have on welfare as there are several opposing forces. Free entry results in a greater variety of goods and higher tax revenues, both of which tend to increase welfare. How- ever, free entry also results in higher costs, higher prices, and lower profits. These three effects will tend to decrease welfare. The simulation results indicate that the variety and revenue effects tend to dominate as free entry results in higher welfare despite the increased costs of production.'

6. SENSITIVITY AND ADDITIONAL SIMULATIONS

Sensitivity analysis reveals that the basic results are robust to a fairly wide range of parameter values. All parameters and data in the model were varied over a reasonable range and, in every case, the results are essentially the same as the base case: free entry leads to firms producing on a small scale with higher costs and thus charging higher prices. Nevertheless, free entry still raises overall welfare as entering firms provide consumers with more variety. Table C3 in Appendix C shows the ranges used for the sensitivity analysis. One notable deviation from this pattern is that if there is very little product differentiation then prices actually fall with free entry. For instance, if o,. is set at 7 and o i s set at 4 and all other parameters are at their base case values, then the calibration procedure calculates o, = 10.7. With these fairly homogeneous goods, free entry results in far fewer firms entering as N = 5 and M = 3.8. Compared with the status quo these firms will have small production runs and higher costs, but due to the lack of product differentiation they are unable to charge higher prices. Even with the hlgh degree of substitutability in this case, free entry still results in higher welfare.

In our previous paper we noted that it was possible for welfare to fall with a policy of free entry. However, we have not found an instance where this happens in our calibration model. Recall that, in our first paper, we were free to select all parameter values as we did not calibrate the model. However, in the current calibrations some of the parameters are constrained as they are

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determined by the data. Furthermore, the previous results were obtained in a model where entry was opened to either home or foreign firms but not both simultaneously while our calibration model allows for simultaneous free entry. Hence the experiments in the previous paper were much more controlled as we not only selected all parameter values but also dictated where entry would come from. Our inability to generate a situation where welfare falls in the calibration model seems to suggest that the Indian auto industry is not likely to experience a decline in welfare as a result of a policy of free entry.

Another policy issue of interest is that of tax reform. The Indian automobile industry is subject to a 40 per cent excise tax on the purchase of all vehicles. Due to the magnitude of the tax one might think that this is simply bad policy with adverse welfare implications. Tables C4 and C5 of Appendix C present the results of the tax reform simulations for the status quo number of firms and the free entry number of firms respectively. What is striking is how little tax reform impacts welfare. With the existing number of firms, a 50 per cent reduction of the tax only increases welfare by less than 1 per cent and there is only a 6 per cent gain in the free entry case. Apparently, the dead weight loss triangles resulting from the tax are rather small compared with consumer surplus. The explanation for the small welfare effect of the tax in the status quo number of firms case is rather intuitive and is perhaps easiest to think about in terms of a tax increase. With a concave utility function and a fixed number of firms, a tax increase eliminates the consumption of the units with the lowest marginal utilities and thus the consumer surplus loss is rather small. When free entry is considered, a tax increase has larger effects because it results in some firms exiting and thus some of the units with the highest marginal utilities are no longer consumed. We should also note that the small welfare gain is probably in part due to the fact that we have calibrated the model with a relatively low elasticity of demand. With higher demand elasticities one finds that there are more significant welfare gains associated with a 50 per cent tax cut. Figure 1 shows that the welfare gains from tax liberalization grow exponentially with the overall elasticity of demand.

On the other hand, note that tax reform does have a substantial impact on total output. In the free entry case the tax reduction results in a 13 per cent increase in total market output. This is a rather interesting result given the usual justification for the excise tax. Recall that the explanation of such. policies in India is typically that the taxes are in place to discourage the consumption of luxury goods. In light of this, and the fact that pollution and congestion are growing problems in India, our simulations suggest that this may not be as bad a policy as one might think. The tax is effective as it reduces consumption of the good but only causes minor welfare reductions.

Lastly, we investigate the effect of giving more weight to tax revenue in the welfare equation. This higher weight is usually thought of as reflecting the dead weight loss of alternative sources of revenue. If we increase the weight from 1 to 1.1 then the status quo case with a 40 per cent tax actually yields

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2 ((I C

I c .- ((I 0)

1.05 1.2 1.4 1.7

Demand elasticity

Figure I Welfare gain from a 50% tax reduction.

higher welfare than the status quo number of firms with a 20 per cent tax. Likewise, a weight of 3.2 is enough to raise the free entry welfare with a 40 per cent tax above the welfare obtained in free entry with a 20 per cent tax. This is further evidence that the excise tax appears to be a rather innocuous policy for the Indian market.

7. CONCLUSIONS

Our results indicate that free entry should raise total Indian welfare. The results also suggest that free entry in the Indian automobile industry is likely to result in a substantially larger number of firms operating on a smaller production scale with higher costs. The later result appears to be consistent with recent events in the Indian market as there has been a large increase in the number of auto producers in recent years. However, as we already noted, our model did not predict the large increase in production capacity that has occurred. Tlus is primarily due to the fact that the CES form considered tends to place greater weight on increases in the number of varieties as opposed to increases in overall consumption. In addition, our results suggest that the excise tax seems to have surprisingly small adverse welfare consequences and, with the current number of firms in the industry (number of firms in 1993), can be justified by a slightly higher (10 per cent) weight for revenue in the welfare equation.

While Indian automobile prices are high by world standards, they look in line with world prices when excise taxes are adjusted for. Yet labour

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costs are lower in India than in the west. Our results suggest that these relatively high costs may simply be the result of the inability of the firms to produce on a large scale. However, despite the higher costs and prices that result with free entry, welfare still rises as consumers benefit from greater variety.

The Indian experience appears to be different thus far from the experiences of other nations that have pursued a policy of free entry coupled with high tariffs and taxes. In the mid 1970s, a relatively healthy Australian auto industry began to break down.8 Subject to a system of high taxes, high tariffs, and free entry, the industry became fragmented and, as a result, costs and prices rose dramatically. Gregory (1988) notes that the industry became so inefficient that buyers at the margin were prepared to pay a 90 per cent import tariff for a foreign car. The Indian industry has been operating under similar policy conditions since the industry de-licensed in 1993 and yet we do not see this type of fragmentation of the ind~s t ry .~ Three possible explanations come to mind. One is that Australia had extremely high domestic content requirements which pushed prices upward. Another possibility is that India's lower labour costs help dampen the adverse affects of a prohibitive tariff. The last possibility, and perhaps the most compelling explanation, is that India's income distribution and its large population make it unique. India has a huge group of consumers who cannot afford to buy a car at current prices. As prices fall,Io due to increased numbers of firms and access to foreign technology, demand may increase rapidly as people other than those in the upper tail of the income distribution begin to demand cars. However, for such entry-level cars, profits per car are small so that one would expect less entry and larger capacity as seems to have occurred in the Indian case.

In terms of future work, attempting to measure the elasticity of demand and the distribution of reservation prices in the Indian car market and examining the welfare implications for free entry would be interesting considerations and may shed some more light on why the liberalization in India appears to be successful.

APPENDIX A

Table A1 Production and price data for Indian cars

Make Quantity (1993) Retail price before excise tax (Rupees, 1994)

Hindustan- Ambassador 22 128 153 400 Premier-Padmini & NE118 20 958 144 411 Mahindra-Jeep 39 657 246 700

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Table A2 Production and price data for foreign cars

Make Quantity (1 993) Retail price before excise tax (Rupees 1994)

Hindustan-Contessa Telco-EstateISierra Maruti-Cars Maruti-Vans &Jeeps

APPENDIX B

The cost structure used in the calibration is derived as follows. We first pin down a range of values for AFC and AVC by examining sales and cost data for two Indian manufacturers. We then derive general expressions for AFC and AVC as functions of quantity produced. Lastly we calibrate the general cost functions to our observations on Indian costs.

Data relating costs to net sales for Hindustan Motors and TELCO in 1982-1983 were obtained from Aggarwal (1988) and are presented in Table B 1.

Table B1 Cost Breakdowns-Year: 1982-1 983 Data in 100,000 Rupees

Components Hindustan TELCO

Materials Wages and salaries Depreciation interest Net Sales

Taking variable costs (VC) to be the sum of materials and wages and fixed costs (FC) to be the sum of depreciation and interest payments we can now express VC and FC as a percentage of net sales. Doing so suggests that VC accounts for 81.8 per cent of net sales and FC accounts for 5.7 per cent for Hindustan. The data for TELCO suggest that FC are 7.8 per cent of net sales and VC are 83.6 per cent. The remainder of net sales is assumed to be net profits, which suggests that for Hindustan net profits were 12.5 per cent of net sales while net profits for TELCO were 8.5 per cent of net sales. For our base case calibrations we select costs on the high side of these ranges: k,,= 0.84 and kf = 0.09 where k,, and kf denote the percentage of price attributed to variable costs and fixed costs respectively. This provides us with a point on both the fixed and variable cost functions we seek and all that remains is to determine how these costs vary with the scale of production.

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Free entry in the Indian automobile industry 45 1

In order to determine how costs change with the scale of production we exploit the data from a study based on the British automobile industry. Pratten (1971) examines capital, labour, and material costs on a per unit basis for various size plants. His data are reported in Table B2." Taking the sum of material costs and labour costs as variable costs and the remainder as fixed costs, these data enable us to estimate two functions: AVC as a function of quantity and AFC as a function of quantity. As one would expect, both of these costs decrease as the scale of production increases. Plotting the data suggests that a constant elasticity curve is an appropriate curve to fit to the data.

Table B2 Per unit costs in pounds sterling

Scale of production 100 000 250 000 500 000 1000 000

Initial fixed cost 3 8 20 14 10 Material cost 265 250 240 235 Labour cost 102 90 86 85 Capital cost 60 5 3 50 48

The data are fit to cost equations (25) and (26). In these equations, the parameters 116, and llbf are the elasticities that describe how the costs change as q changes. Taking logs of these equations provides us with a log-linear equation which enables us to obtain estimates of b, and by The regression results are given in Table B3.

Table 83 Elasticity estimates

Variable costs Fixed costs

B" t-stat RZ Obs

0.0605 bf 0.227 6.7 t-stat 7.3 0.96 R2 0.96 4 obs 4

To complete the cost functions we need to determine the values of a, and a/ that are appropriate for the Indian industry. The above cost functions are calibrated to the Indian market by using our observation on Indian costs. For variable costs we can rewrite the above equation as a,, = (AVC)qbv, where AVC=(0.84)(price) in our base case. With values for the four parameter in the cost functions, AVC and AFC are simply a function of the scale of production.

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APPENDIX C

Table C1 Base case calibration results

Table C2 Base case simulation results

Status quo Free entry

Home Foreign Home Foreign

Number of firms 3 2 4.8 18.3 Per firm output 27 581 80 543 4027 12 900 Producer price 195 815 166 092 212 068 178 521 AVC 164 484 139 517 184 792 155 866 AFC 17 623 14 948 27 276 22 655 Indian welfare 6.197~10" 6.664x101' -

Table C3 Parameter ranges for sensitivity analysis

Parameter Min. Value Max. Value Parameter Min. Value Max. Value

Kt. 0.79 0.90 kf 0.07 0.11 E 1.05 2.5 tax 0 0.4 0 2.5 3.7 0s 2.6 4 B,, 0.03025 0.09075 Bf 0.1135 0.3405 N 2 4 M 2 4 V 176 234 215 397 w 149 483 182 701 Q I 74 505 91 062 Q2 144 978 177 194

Table C4 Tax simulation results for status quo

Status quo tax = 40% Status quo tax = 20%


Number of firms 3 2 3 2 Per firm output 27 581 80 543 3 1 347 91 540 Producer price . 195 8 15 166 092 203 359 172 491 AVC 164 484 139 517 163 216 138 441 AFC 17 623 14 948 17 119 14 520 Indian welfare 6.197~10" - 6.207~10"

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Table C.5 Tax case simulation results for free entry

Free entry tax = 40% Free entry tax = 20%


Number of firms 4.8 18.3 5.5 85.7 Per firm output 4027 12 900 1102 3293 Producer price 212 068 178 521 236 459 200 177 AVC 184 792 155 866 199 858 169 289 AFC 27 276 22 655 36 601 30 887 Indian welfare 6.664~10" - 7.069~10'~ -

APPENDIX D

Let QH and QF denote total output of the home and foreign sectors

respectively. We can then define market shares: 9 = Q H

and Q H + Q F

(1- 9) = Q F . We can write the Herfindahl numbers-equivalent for

Q H + Q F

the total market as follows:

where SiH and SiF are the firms' shares within their respective sectors. Let the numbers-equivalent for the home and foreign sectors be given by (1IA) and (11B) respectively. Now NT is given by:

If NT is less than (Nf iN , ) then it implies that:

This can be rewritten as:

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Grouping terms and simplifying yields:

Factoring implies:

which must be negative as the denominator is positive. Thus N,<(N,+N,.).

ACKNOWLEDGEMENTS

The authors thank Mr S. S. Marathe, Mr S. Duda, Ms Nag, and Ms M. Krishna for their assistance in locating data, and IRIS at The University of Maryland for partial funding of this project. Thanks also to Chris Dulnler for his helpful comments.

NOTES

1 See Jensen and Krishna (1996) 2 See Krishna et al. (1989) for more details on these derivations. 3 This follows from the fact that price equals marginal cost for good Sand thus

4 Note that both the variable and fixed costs depend on the level of output. The reason for this is that we need the fixed costs to vary with the size of the plant for the simulations that follow. This is necessary to capture the idea that larger plants generally have larger fixed costs. However, it is important to note that in the derivation of the firm's first-order conditions the fixed costs are taken as given and thus they do not enter into the firm's maximization problem.

5 Note that as products are differentiated this is consistent with positive profits. 6 See ICRA reports at http:Nwww.icraindia.com/ 7 As noted earlier, the 'foreign' firms are often joint ventures with lndian firms and thus

some of the foreign profits should be included in the home country welfare calcula- tion. This makes no qualitative difference in the results as profits are a small portion of total welfare.

8 See Albon (1 995) and Gregory (1 988). 9 Two differences between the Australian and Indian cases should be noted. Australia

just had high tariffs on imported cars, while importing automobiles is essentially not permitted in India. Also, Australia had significantly more varieties of automobiles prior to liberalization than India did.

10 Recall that, in our model, the nominal prices of automobiles rose as a result of free entry. However, the price increase is largely due to the increased variety of cars. The falling prices referred to here are 'variety adjusted prices'. We know that the variety

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adjusted prices are falling because total market demand and welfare are both rising. 11 This is Pratten's data as reported in Aggarwal(1988).

REFERENCES

Aggarwal, R.N. (1988) 'Indian automobile industry: problems and prospects'. The Indian Economic Journal 36(2), 50-61.

Albon, R. (1995) 'The future of Australia's passenger motor vehicle industry'. Mimeo, Australian National University.

Brown, D.K., Deard0rffA.V. and Stem R.M. (1995) 'Estimates of a North American Free Trade Agreement'. In Kehoe, P.J. and Kehoe T.J. (eds) Modeling North American Economic Integration. Advanced Studies in Theoretical and Applied Econometrics. London: Kluwer Academic

Centre for Monitoring Indian Economy (1996) 'India's Industrial Sector'. January, 309-24.

De Melo, J. and Tam, D. (1992) A General Equilibrium Analysis of US Foreign Trade Policy. Cambridge and London: MIT Press.

Dixit, A.K. (1988) 'Optimal trade and industrial policy for the U.S. automobile industry'. In Feenstra, R. (ed) Empirical Methods for International Trade. Cambridge, MA: The MIT Press.

Dixit, A.K. and Stiglitz, J.E. (1977) 'Monopolistic competition and optimum product diversity'. American Economic Review 67,297-308.

Gregory, R.G. (1988) 'A sad and sorry story: industry policy for the Australian motor vehicle industry'. In Spence, A.M. and Hazard, H.A. (eds) International Competitive- ness. Cambridge, MA: Ballinger Publishing Co.

Harrison, G.W., Rutherford, T.F. andTam, D.G. (1997) 'Quantifying the Uruguay Round'. Economic Journal 107, 1405-30

Jensen, P. E. and Krishna, K. (1996) 'Entry policy in an open economy'. Indian Economic Review XXXI(1). 41-56.

Krishna, K., Hogan, K. and Swagel, P. (1989) 'The non-optimality of optimal trade policies: the US automobile industry revisited, 1979-1985'. NBER Working Paper No. 31 18.

Lopez-de-Silanes, F., Markuson, J.R. and Rutherford, T.F. (1994) 'The auto industry and the North American Free Trade Agreement'. In Francois, J.F. and Shiells, C.R. (eds) Modeling Trade Policy: Applied General Equilibrium Assessments in North American Free Trade. Cambridge: Cambridge University Press

Mankiw, N.G. and Whinston, M.D. (1986) 'Free entry and social inefficiency'. Rand Journal of Economics 17 (1). 48-58.

Pratten, C. (1971) 'Economies of scale in machine tool production'. Journal of Industrial Economics 19,148-65.

Rodrik, D. (1988) 'Imperfect competition, scale economies, and trade policy in develop- ing countries'. In Baldwin, R. (ed) Trade Policy Issues and Empirical Analysis. Chicago, IL: The University of Chicago Press.

Spence, A.M. (1976a) 'Product selection, fixed costs, and monopolistic competition'. Review of Economic Studies 43,217-36.

Spence, A.M. (1976b) 'Product differentiation and welfare'. American Economic Review 66,407-14.

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Free entry in the Indian automobile industry: a calibration model