Problem Set I

Macroeconomics 201213 (MurphyDeMicco) This version: 13 March 2013

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Problem Set I

Macroeconomics Academic Year 2012-2013 BIEMF

Solutions

(To exercises NOT discussed in class, Part 1)

CHAPTER 5 Goods and financial markets: The ISLM model

Exercise 33 The IS and LM model Consider an economy characterized by the following behavioural equations:

a) What is the effect of a reduction in the sensitivity of investments to income on the

position/slope of the IS curve? Show graphically and provide an economic explana-tion for your answer.

b) What is the effect of an increase in sensitivity of money demand to the interest rate on the position/slope of the LM curve? Show graphically and provide an economic explanation for your answer.

Solution: a) The IS curve is described by the following equation:

GidYdTYccY o +++= )()( 211

from which:

Yd

dcTcGcd

i2

1110

2

1)(1 +=


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Movements in d1 modify the slope of the IS curve (but not the intercept). In particular, d1 makes it steeper (IS). Now if we have i I Y I (but the decrease in I is weaker in the IS case) Y (but the decrease in Y is weaker in the IS case)

b) The LM curve is described by the following equation:

ifYfPM

21 =

from which:

Movements in f2 affect both slope and intercept of the LM curve. In particular, f2 makes the curve flatter and lifts up the intercept. Indeed, given a variation in income,


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the variation of the interest rate necessary to bring the money market back into equi-librium is smaller the higher is the sensitivity of money demand to the interest rate.

Exercise 34 The ISLM model, monetary and fiscal policies Suppose that the macroeconomic system of country B can be described by an ISLM model. a) Describe graphically the adjustment process towards a new equilibrium in the case

where the government carries out an expansionary fiscal policy and simultaneously the monetary authority implements a policy aimed at maintaining a fixed interest rate.

b) Now consider a country C, identical to country B apart from the fact that it is char-acterized by a greater sensitivity of money to income (that is, if for both countries, it is the case that f1(C) > f1(B)). If a fiscal policy of the same size as the one mentioned in point a) were introduced in country C, how would the equilibrium values of Y and i change? Compare the two scenarios with the aid of a graph.

Solution:

a) An expansionary fiscal policy shifts the IS curve right increasing both equilibrium

income and the interest rate (from B to B). To contrast this effect, the Central Bank must carry out an expansionary monetary policy aimed at leaving the interest rate unaffected, and moving the LM curve downwards (to reach B). The new equilibrium is characterized by a higher income.

b) The LM curve of country C has a higher slope, since a given variation in income gen-erates a greater variation in the interest rate necessary to maintain the financial market in equilibrium. This is due to the fact that money demand is more sensitive to income. A fiscal policy like the one in point a), for country C generates a greater in-crease in the interest rate as a consequence of the rise in income with respect to B. Therefore the final impact on equilibrium income is inferior in country C (fiscal pol-icy is less effective).


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Exercise 35 The money multiplier and the ISLM model a) Write down the formula of the money multiplier and explain the meaning of the

variables involved in its formula. Suppose that the central bank reduces the coeffi-cient of the reserves. Explain in detail the effects of this policy on the supply of money.

b) Suppose now that, starting from an equilibrium point in the standard ISLM model, the demand for currency of its citizens decreases. Show graphically how the ISLM model changes. Explain in detail the adjustment process to reach the new equilibrium point. In particular, discuss the effects on investment, I.

Solution: a) Expression for the money multiplier is , where c stands for the rate of

demand for currency that individuals would like to hold while stands for the re-serve requirement for the banks. A reduction of would increase the amount of money available for banks to lend, consequently the money in circulation would in-crease as a result of an increase in the money multiplier

b) A reduction of the demand for currency leads to an increase of the money multiplier, hence to an increase in the money supply. LM curve shifts right to LM characterized by a lower interest rate, which results in an increase in investment and aggregate demand.


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Exercise 38 The ISLM model and the right policy Consider a closed economy represented by the following equations:

a) Write the equations for both the IS and LM curves, indicating slopes and intercepts.

Represent them in a graph.

b) Compute the equilibrium level of income and interest rate (in percentages) and indi-cate them in the previous graph. If the government of this country wants to increase the interest rate, keeping constant the level of output, what policy mix would you suggest? Explain and represent your suggestions in the previous graph.

Solution: a) For the IS we have that

Hence we can rewrite this as or , so the vertical inter-cept is 7.2, the horizontal intercept 900 and the slope 0.008. For the LM, on the other hand, we have that:


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Which can be rewritten as , giving a vertical intercept of -50, an hori-zontal intercept of 625 and the slope 0.08.

b) The equilibrium is given by the intersection of IS and LM (E1 in the graph below):

If the government of this country wanted to increase the rate of interest, while main-taining the level of income and production, it may act through the following combina-tion: expansionary fiscal policy + contractionary monetary policy. In this way the IS would move to the right and the LMup: the economy will jump from equilibrium E1 to E2.

Exercise 40 The ISLM model and the sensitivity of demand for investment An economy is described by the following equations: IS:

LM:

where all variables have the usual interpretation. Due to an economic crisis, the sensi-tivity of demand for investment goods with respect to production increases. a) Starting from an equilibrium, show graphically and analytically the effects of such

an increase. Does the multiplier of aggregate demand increase? Explain.


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b) The Governor of the Central Bank claims The increase in the sensitivity of invest-

ment with respect to production reduces the effectiveness of an expansionary mone-tary policy. Is this statement true? Explain also graphically by describing the ef-fect of a bond purchase on interest rates and output before and after the change of sensitivity.

Solution: a) In order to understand how IS changes, we express the interest rate:

2

10

2

11 )()1(d

GITccY

ddci

+++

=

An increase in d1 makes the IS curve flatter. The multiplier increases because any change in autonomous spending has a stronger effect on production than the initial change in investment

b) A purchase of bonds on the open market by the Central Bank represents an expan-

sionary monetary policy and leads to an increase in the quantity of money. As a con-sequence the LM curve shifts to the right (LM). The output increases and the interest rate falls. With a flatter IS curve, the same operation has a stronger effect on output and a weaker effect on the interest rate. Therefore, Governors statement is incorrect.


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Exercise 42 The ISLM model

a) In a closed economy government spending G and net taxes T are exogenous, and consumption and investment are described by the usual behavioural equations. As-suming that the demand for money has a sensitivity to income close to zero, repre-sent graphically the IS and LM curves. Explain in detail if and why the curves are different from the standard ISLM diagram.

b) Assume and . Represent graphically in the dia-

gram above the effects of a decrease in the autonomous investment spending by and explain economically how this change affects equilibrium output and in-

terest rate. Calculate the change in equilibrium output by using the concept of the multiplier , and explain your answer. Finally, explain if the change in output is equal, larger or smaller than the change in output the economy would have had in the case of a standard sensitivity to income of the demand for money.

Solution:


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a) The IS will have the usual form and slope: An increase in the interest rate reduces the

demand for investment and the production and so the IS curve has a negative slope. The LM curve will be different from the standard case, because it becomes almost horizontal. If the demand for money is nearly not sensitive to income (f1 close to zero), after a small increase of the interest rate, production must increase enormously to bring back to balance the money market.

b) The reduction in autonomous investment will shift the IS to the left by an amount which is equal to the change in autonomous spending times the income multiplier. Given that the LM is quasi horizontal, output will fall by (nearly) the same amount and the interest rate will remain (nearly) unchanged. The reduction in output in this economy is larger than the reduction observed in the standard case with a positively sloped LM curve. In the latter case a reduction in the interest rate would have stimu-lated investment, and this would have reduced the recessionary effect of the decrease in autonomous investment. In the standard case, a reduction in output would lead to a reduction in the demand for money and a reduction in the interest rate. In this economy, however, the demand for money is almost insensible to changes in output and therefore the interest rate will not be affected (or it will fall by a negligible amount).

Exercise 43 The ISLM model and the recession a) Consider a closed economy. In the previous year the autonomous component of con-

sumption has decreased. Use the ISLM model to explain what the Central Bank has to do in order to avoid a recession? Compare the new investment level (after the Central Bank intervention) with the initial equilibrium (after the reduction in autonomous component of consumption). Motivate your answer.

b) In order to avoid the recession, what can the government do? Compare the composi-

tion of the aggregate demand (after the government intervention) with the initial equilibrium (after the reduction in autonomous component of consumption).

Solution: a) If the autonomous component of consumption is reduced, the IS moves to the left.

Both the income and the interest rate go down. To avoid recession, the Central Bank could implement an expansionary monetary policy, which will cause a further reduc-tion of interest rate and a compensatory increase in income (which for example may be equal to the initial level). Comparing this new equilibrium with the initial one of we see that components of consumption have declined while that of investment in-creases as a result of reduced interest rate.


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b) The government can intervene to avoid recession by increasing public expenditure or reducing taxation. This will shift IS back to its initial position, maintaining income and interest rate unchanged. The level of investment would be lower than the one found in point a).

Exercise 45 The ISLM model True or False? Explain whether the following statement is true or false. Motivate your answer in a brief but rigorous way, by making explicit reference to the relevant theory. Lack of proper explanations will result in zero points.

In a closed economy with constant prices, a tax cut will increase the equilibrium in-come by an amount that is going to be larger the higher the sensitivity of the demand for money to the interest rate. Solution: True. The more sensitive the demand for money to interest rate, the more 'flat' is the LM, and it is immediate to verify graphically that, in the presence of a flat LM, the rightward shift of the IS caused by a reduction in taxes leads to an equilibrium in which the income increases more than it would in the presence of a relatively steep LM. To understand why this is true, you must follow the sequence of events triggered by the reduction of taxes T. When T is reduced, the disposable income increases, and with it the demand for consumption, aggregate demand and production in the goods market. But we must also take into account the fact that, in the money market, this higher Y leads to an increase the interest rate. The increase in the interest rate in turn affects the goods market by reducing investment demand and mitigating the initial increase in aggregate demand and production. The latter effect, which scales the initial expansionary effect of the reduction of T, will be greater the greater the increase in the interest rate on the money market. In particular, if the demand for money is very sensitive to interest rate, the interest rate will have to increase by only a little in order to bring the market back to the equilibrium, and in the goods market demand and production will eventually in-crease a lot.


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Exercise 46 Increase in c and open market operations a) Citizens in country BETA begin to cast serious doubts about the good health of fi-

nancial institutions in their country. For this reason they decide, as a precautionary measure, to withdraw part of their deposits and keep a larger share of their money as currency. Following your books notation, this means that the parameter c in-creases. Using the IS-LM model, represent graphically the effects of such change in c on income and interest rate, defining in details how and why it affects macroeco-nomic equilibrium.

b) In order to lead income back to its initial level, BETA Central Bank decides to en-gage in an open market operation. Define the meaning of open market operation. Which specific operation is needed in this case, given the objective of the Central Bank?

Solution: a) The parameter c appears in the equation defining the money multiplier

1(1 )

mmc c

=+

Given that M= mmH, where M represents the money supply and H the monetary base, and given that the money multiplier mm is lower the higher is c, and increase in c will lead ro a decrease in M and to a leftward shift in the LM. Indeed, if deposits decrease, financial institutions will be able to offer a lower volume of loans, thus de-posits will decrease further and so will the money supply. In the new equilibrium (point E2 in the graph), the interest rate will be higher and the income will be lower. Indeed, the reduction in the money supply due to the increase in c induces an excess of demand and an increase in the interest rate. Given that I is higher, demand for in-vestments will decrease and so will production in equilibrium.

b) An open market operation (O.M.A.) is the purchase or sale of government bonds by

the Central Bank for the purpose of increasing or decreasing the money supply. A purchase of bonds increases the money supply, while a sale of bonds decreases money


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supply. In this case the central bank must purchase bonds. The volume of the inter-vention must be such that the LM goes back to its initial position and the income is back to the level observed before in the increase in c.

Exercise 47 The ISLM model and the liquidity trap True or False? Explain whether the following statement is true or false. Motivate your answers in a brief but rigorous way, by making explicit reference to the relevant theory. Lack of proper explanations will result in zero points. If an economy is in the liquidity trap, fiscal policy cannot influence the equilibrium output. Solution: False. When the economy is in a liquidity trap, the intersection between IS and LM is on the horizontal part of the LM curve. In this situation, monetary policy (or at least tradi-tional monetary policy) cannot affect the equilibrium output. On the other hand, the fiscal policy is very effective. In fact, if the LM is horizontal, an expansionary fiscal pol-icy does not affect the equilibrium interest rate. The variation of the equilibrium output is for a shift of the IS curve largest in this case. Exercise 49 The ISLM model and a decrease in the reserve ratio a) Consider the standard IS-LM model. Suppose that the Central Bank reduces the re-

serve ratio. Show graphically how the IS-LM equilibrium changes. b) Explain the adjustment process in order for the economy to reach the new equilib-

rium level. What are the effects of this monetary policy on investments? Solution: a) Graphically we have:


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b) If decreases, then the aggregate money supply increases as it increases its leverage of money. Graphically, the LM will shift rightward. At point E, the economy is now in financial disequilibrium. In particular, there is excess money supply that implies that excess demand for bonds and then a lower interest rate (up to point a). Given the lower interest rate, the aggregate investments component increases and with it, ag-gregate demand and income increase. The increase in income stimulates demand for currency, so the interest rate tends to increase in moving from point A to the new equilibrium E. In the new equilibrium, the interest rate decreases and income in-creases. Since investment depends positively on income and negatively on interest rate, ( ; )I Y i increases.

Exercise 50 The ISLM model and fiscal policy The economy of country Lux is described by the following relations:

a) Compute the equilibrium values of income and the interest rate. b) Derive the multiplier of fiscal policy. c) Compare the effects on the equilibrium income of the two different expansionary fis-

cal policies: an increase in government expenditure by an amount of 500 and a con-traction of taxes by 500.

d) Explain the economic intuition. Graphically represent the previous results describ-ing the adjustment process.

Solution: a) Equilibrium requires that both markets (the goods and money markets) are in equi-

librium. The goods market equilibrium requires Y = Z = C + I + G, hence

Money market equilibrium requires M/P = L(Y,i), hence:


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The solution to the system of two equations is then Y = 6,250, i = 0.125 = 12.5%.

b) The fiscal policy multiplier is defined by:

c) If we want to assess the change in the equilibrium output of a change in government

spending:

1.25* 1.25*500 625Y G = = = Hence we fid that Y(G) = 6,875. If, on the other hand we look at the change in taxes of the same amount:

( ) ( )( )11.25 1.25 0.3 500 187.5Y c T = = = The end result is that Y(T) = 6,437.5.

d) An increase in public expenditure G implies a increase in production and the IS curve shifts to the left to IS(G). The economy moves along LM until reaches the new equilibrium at point 1. A reduction in taxes T implies an increase in the disposable income (Y-T) and so an increase in consumption and production. The IS curve will shift left to IS(T). The economy moves along LM until it reaches the new equilibrium at point 2. The effect of a fiscal expansion is greater in the first case (the IS moves tp a higher position) since a change in G directly affects autonomous expenditure, while a change in taxes only indirectly affects the production (though disposable income and consumption, the effect is weighted by c1)


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Exercise 51 The ISLM model and governments policies Consider an economy characterized by the following equations:

a) Determine the equilibrium levels of Y and i . b) Describe and show graphically the governments possible policies if it wants to in-

crease output keeping the level of interest rates constant. c) Would a simultaneous increase of 100 in G and T leave the equilibrium output

level unchanged? Motivate your answer. Solution: a) The goods market equilibrium requires Y = Z = C + I + G, hence

120 0.3( 150) 0.2 1,500 200Y Y Y i= + + +

1 (275 1,500 ) 550 3,000

0.5Y i i= =

The LM, on the other side, is given by:

d sM MP P

=

0.6 1,200 90Y i =

0.6 901,200 1,200

i Y=

Hence in equilibrium we have

Y = 310 and i = 8%.

b) In order to achieve an increase in output without changing interest rates, the gov-

ernment needs to impose a mix of fiscal and monetary policies, shifting both the IS and the LM curve: LM0 to LM1 and IS0 to IS1.


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c) Clearly output increases. A change in government expenditure G increases output proportionally, while the change in taxes T has a smaller effect on output. Thus, a simultaneous increase in taxes and expenditure of 100 increases toral autonomous expenditure by

1 1 1(1 ).100 70G c T G c G c + = = = And output by:

11

1 1 22

1 ( ) 0.8*70 56(1 )

Y G c Tfc d df

= = = +

Exercise 52 The ISLM model and an increase in investment The macroeconomic situation of country Maux is as described by the following graph:


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a) The government wants to increase the level of private investment, but it does not want to change output. What policy mix (fiscal and monetary policies) needs to be chosen? Out of the four following options, mark the best policy mix and show its ef-fects graphically.

- Monetary and fiscal expansion - Monetary contraction and fiscal expansion - Fiscal contraction and monetary expansion - Fiscal and monetary contraction

b) Illustrate the adjustment process that brings the economy to its new equilibrium

and explain how the composition of demand changes. Solution: a) The correct policy mix is a fiscal contraction combined with a monetary expansion as

displayed in the graph below:

b) The fiscal contraction shifts the IS curve down to IS, while the monetary expansion shifts the LM curve to the right (LM). The new equilibrium is given by point 2. The new equilibrium outcome is the same as before, but the reduction in the interest rate increases private investment which in turn compensate for lower private or public expenditure, depending on whether the government decides to increase taxes or re-duce expenditure.

CHAPTER 7 The labour market

Exercise 53 Definitions Explain, briefly and rigorously, the difference between employment rate and participa-tion rate Solution:


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Employment rate is the ratio of the number of people who are employed to the number of people in the labour force. The participation rate is the ratio of the labour force (that is, how many people are working or are looking for a job) to the total population of working age (that is, how many people could be working). Exercise 55 The labour market In an economy, the wage setting equation (WS) is given by , while the price setting equation (PS) is . The parameter defines the degree of centralization of contract negotiations. a) Knowing that and , compute the equilibrium level for the natural

rate of unemployment and for the real wage.

b) Suppose that now the target for the natural level of unemployment by the govern-ment is equal to 6%. Which kind of mechanism for the contract negotiations should be implemented? Explain your answer.

Solution: a) We know that the wage setting equation is W/P = 8 ut, whereas the price setting is

determined by W/P = 1/(1 + ) = 0.83. Equalizing WS to PS we get that 0.83 = 1.5 8 un. Hence, un = 8.375%.

b) The governments objective is un* = 6%. Setting WS = PS, we get 0.83 = 8 un* . That is, 0.83 = 8 0.06 => = 1.31 < 1.5. To reduce the natural rate of unem-ployment, government has to reduce the degree of centralization of contract negotia-tions. A reduction of the degree of centralization lowers the bargaining power of the workers, and hence, results in a shift of WS curve to the left to a lower level of natural rate of unemployment.

Exercise 56 The labour force, participation rate and unemployment rate a) In 2006 the population of a country was 1,600,000 inhabitants, one million were em-

ployed and 200,000 were unemployed. Compute the labour force, the participation rate, and the unemployment rate.

b) In 2007 the population was unchanged; the unemployment was 10%, and the out of the labour force population increased by 200,000 people. Recompute the participa-tion rate and the unemployment rate. If 110,000 formerly occupied become retired and only 10,000 young people enter the labour market, by how much would the dis-couraged workers have increased?

Solution: a) The labour force is the sum of employed and unemployed, that is, in our case

1,200,000 people. The participation rate in the workforce is the relationship between labour force and total population, that is, in our case (1,200,000/1,600,000) = 75%.


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The unemployment rate is the ratio between the number of unemployed to labour force, that is (200,000/1,200,000) = 16.6%. The nonemployment rate is the ratio be-tween the employed and the total population, i.e. (600,000/1,600,000) = 37.5%.

b) In this case the workforce is reduced to one million units, namely the participation

rate will change to (1,000,000/1600,000) = 62.5%. Given that the unemployment rate is 10%, the employment fell to 900,000 and unemployment became 700,000. Then, unemployment rate is equal to (700,000/1600,000) = 43.75%. The discouraged work-ers are those who give up looking for work. If the workforce was reduced by 200,000 units, 110,000 workers have retired and 10,000 young people entered the labour mar-ket, 100,000 people left voluntarily from the job market.

Exercise 57 The labour market Consider the following labour market. The WS equation is: . The production function is Y = N, and the nominal wages are W. The mark-up is , and z = 1. a) Compute the natural rate of unemployment and the real wages in equilibrium. Sup-

pose now that the production function becomes Y = (3/2)N (that is, in order to pro-duce one unit of output, only 2/3 units of labour are needed). How do the natural rate of unemployment and the real wages change in equilibrium?

b) Return to the case where Y = N. The government proposes to the unions to reduce the unemployment insurance, z, from 1 to 2/3. In exchange, the government will im-plement policies towards more competition and reduce the mark-up, , from 1 to 3/4. The unions are interested in the real wage (they prefer it higher) and in unem-ployment (they prefer it lower). Will the unions accept the proposal from the gov-ernment?

Solution: a) If the markup equals to 1 then the PS curve is W/P = 1/(1+1) = 1/2. To find the

natural rate of unemployment we have Pe = P. As a result WS becomes W/P = (3/8)(2 u). By equating PS and WS we have (3/8)(2 u) = 1/2 and un = 2/3. Real wage is W/P = 1/2. When the production function changes, the unit cost be-comes (2/3) W so now, P = (2/3) W (1+1) = (4/3) W or W/P = 3/4. By inserting this level of real wage in WS we get un = 0.

b) Now the PS curve becomes W/P = 4/7 while WS curve becomes W/P = (3/8)((5/3) u) = (5/8) (3/8) u. We obtain un = 1/7. Given that real wages rose and unem-ployment fell, the union will accept the proposal.

Exercise 59 Product market competition True or False? Explain whether the following statement is true or false. Motivate your answer in a brief but rigorous way, by making explicit reference to the relevant theory. Lack of proper explanations will result in zero points.


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Since the economy tends to return to the mediumrun equilibrium output , and that differences from this level of production are only temporary, even a permanent shock to aggregate supply, such as the endorsement of a regulation which increases the degree of product market competition, will affect equilibrium output only temporarily. Solution: False. In the medium run the economy will converge to the natural level of output and deviations from this level of production are transitory. However, a permanent shock on the supply side, such as an increase in product market competition, will affect . The PS curve will shift upward and this will lead to a lower natural level of unemployment and to a higher natural level of output. Given that the new will be larger than the ini-tial one, the effect of the shock on the production will be permanent.

CHAPTER 8 Putting all markets together: The AS AD model

Exercise 61 The model ASAD and price expectations Consider an economy in the mediumrun equilibrium. a) Describe the shortrun and mediumrun effects on prices and the interest rate of an

increase in consumers confidence. Describe graphically and explain.

b) Describe the shortrun and mediumrun adjustment of ASAD and ISLM models after an increase in the marginal propensity to consume under the hypothesis that price expectations are Pe = P-2 (i.e. the expected price is equal to the price two peri-ods earlier).

Solution: a) The increase of consumers confidence can be translated into an increase of c0 or c1.

We assume that we have an increase of c0, then: c0 Z Y Md . But, with Ms constant, i will increase. The IS0 shifs upward to IS1. The increase in production, at a given price level, shifts the AD0 curve upward to AD1. (NOTE: For sake of sim-plicity we ignore the shift of the LM in the short run due to the price increase. Graphically LM should move a bit to the left because higher prices will rise the de-mand for money and, given a constant money supply, the interest rate will rise a bit more). The increase in production leads to an increase in employment and thus to a reduction in the unemployment rate. Wages and prices increase as well. In the short run we move from point A to point B, where output is larger than in the natural level (Y1 > Yn), prices increase (P1 > P*) and the interest rate goes up (i1 > i*) Adjustment process then begins (starting from t+1): the rise of output determines a situation where the economy produces more than its natural level. The increase of employment and the expectation of further increases in prices cause increases in wages and price levels. The AS0 is moving to AS2. Why does the production decrease? The rise of prices determines a reduction of the real money stock and hence an in-


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crease of the interest rate necessary in order to restore the money market equilibrium (You can also think in a different way: higher prices increase the demand for money and, given a constant money supply, the interest rate will rise). LM will shift up to LM2. The higher interest rate reduces the investment and consequentially the pro-duction. The adjustment process will end up when the production will be back to its natural level. In Yn, the level of current prices equalizes the level of expected prices and hence there will no more pressure to move the AS further. In the ISLM model, the increase in prices provoke a reduction of the real money stock, LM shift up till reaching the level of natural production.

b) If Pe = Pt-2, the adjustment process will be slower. So if the shock occurred in period 1,

during period 2 the AS curve doesnt change, since workers do not revise their price expectations. In period 3 workers revise upward their expectations. In t+2, the aggre-gate supply curve shifts up. As long as equilibrium output exceeds the natural level of output, the expected price level increases, shifting the AS curve upward, but only every 2 periods. The adjustment process stops when output returns to its natural level. Then the expected level of prices will be equal to the actual price level and there-fore the AS curve will not change anymore. In ISLM, the increase in price level leads to a decrease in the real money stock; interest rate increases and output de-creases. The LM curve shifts upward. Also here the adjustment process stops when output returns to its natural level and the expected level of prices is equal to the ac-tual price level.


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Exercise 62 Competition, the ISLM and the ASAD models The introduction of the monetary union in Europe has produced an increase in compe-tition between firms. a) Describe graphically the consequences of the monetary union on the labour market

equilibrium.

b) Using the ISLM and ASAD framework, analyse the effects on output, prices, and the interest rate, distinguishing between shortterm and longterm effects.

Solution: a) An increase in competition between firms translates into a reduction of (the

markup on costs) P (W/P) . As a consequence the PS curve shifts upwards to PS. The increase in real wages leads to a reduction of the natural rate of unemployment because now a greater number of people is willing to work at the in-creased real wage. The labour market equilibrium shifts from A to B in the graph be-low.

b) Since Y = N, if un Nn Yn . In other words, the reduction in the natural rate of unemployment translates into an increase in production.

In the short run: Starting from point A, the reduction of causes a reduction in prices for every level of production, leading to a shift to the right of the AS curve. The reduction of markup can affect the position of AD both through the investment (the reduction of the markup reduce profits and this can put at risk new investments) and through the consumption (a lower level of prices provoke an increase of consum-ers income). Here we assume that these two effects compensate themselves and hence AD does not move at all. The reduction of prices leads to a reduction of the real money stock and a consequential shift of LM0 toward right in LM1. In the new short term equilibrium, B is characterized by a lower price level and by a greater level of output with respect to the starting point Yn, but still inferior with respect to the new natural level of output, Yn.


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In the medium run: In the period following the shock, the workers will revise down-wards their expectations on prices. The revision of expectations on prices implies a downward shift of the AS. As long as the output level is below the new natural level, prices will continue to decline and output will continue to grow. The AS curve will continue to shift downwards, and so will the LM. When output finally reaches its new natural level, the economy will be in a new mediumrun equilibrium (point MR) characterized by lower level of prices and a higher natural level of production.

Exercise 65 Price levels a) Consider a closed economy of country A which is at its mediumterm equilibrium.

Due to a discovery of an alternative energy source it becomes possible to substitute oil by the new alternative source of energy which has a much lower price. Illustrate graphically and explain the effects on production and price level in the short and medium term.

b) Is it true that consumption is higher and private investment is lower in the new me-

diumrun equilibrium? Explain. Solution:


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a) A reduction in the cost of energy can be interpreted as a reduction in markup (), be-cause production costs fall due to the new technology. A reduction in raises real wages and the natural rate of unemployment falls. As a consequence the natural level of output increases. In the short run the AS will shift downwards (to AS). Since the economy is below its natural level of production, the AS will continue shifting along the AD curve until the economy reaches its natural level of output (with ASMR). In the new medium run equilibrium B the output is higher and prices are lower than in-itially.

b) The statement is true for consumption and it is false for investment. Consumption in-creases due to higher output. Higher output and lower interest rate lead to higher in-vestment in the new medium run equilibrium.

Exercise 67 ASAD model and increases in the reserve requirement ratio An economy closed to international trade and characterized by flexible prices is in equi-librium at full employment.


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a) With the help of the ASAD model, describe and illustrate graphically shortrun

and mediumrun effects of an increase in the reserve requirement ratio on income and price levels.

b) If investments are insensitive to interest rates, increased reserve requirement ratio has no effect on income or prices. True or false? Explain.

Solution: a) An increase in causes a decrease in money supply (decreases the multiplier). In the

short run, a contraction in the money supply implies a shift in the LM line up i I Y. In ADAS model, this change shifts the AD curve to the left (equilibrium B): Y u w P. Shortrun equilibrium (point B), Y < YN e P < Pe. This triggers the adjustment process: Pe the AS curve moves progressively downward P Y . This adjustment continues until Y is less than YN. In the medium run the economy is back to full employment at the same level of interest rates, but at a lower price (new equilibrium at point C). In the medium run monetary policy is neu-tral and produces effects only in the price change that are proportional to the money supply.

b) True. If the investments are insensitive to the interest rate (parameter d2=0), IS is a vertical line. This implies that the AD is vertical: any variation in prices varies the money supply which in turn causes a change in interest rate but this has no effect on I and then Y. In this case, the decrease in money supply resulting from the increase of (restrictive monetary policy) will have no effect on income and prices even in the short run (the vertical AD curve does not move). The only change in the short to me-dium run will be the increase the interest rate.

Exercise 69 The ASAD model Consider an economy that is in a shortrun equilibrium with output Y0 greater than the natural level of output (Y0 > Yn).


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a) In an ASAD diagram represent the shortrun equilibrium and indicate this point with E0. In the same graph show the mediumrun equilibrium to which the economy will converge in the absence of any intervention by policymakers. Call the new equilibrium EN, and explain in detail how and why the economy converges to this new equilibrium. Explain the changes in output and interest rate during the transi-tion towards EN.

b) Assume now that the economy is still in the initial equilibrium E0. In order to

bring the economy immediately back to its natural level, Yn, the government decides to resort to a fiscal policy consisting of a change in the level of government spending G. Should the government raise or reduce G? Show in the graph above the new equi-librium point which will be reached after the governments intervention, and call it EG. Compare the composition of aggregate demand and the interest rate in EG and EN (the mediumrun equilibrium in the absence of any intervention by the govern-ment), and explain the differences, if any, between these two equilibria.

Solution: a) At E0 Y > Yn, and prices are above the expected level, hence wages will start to in-

crease, firms will raise prices due to the increased costs of production and the AS will start moving leftward. In the next period the new short-term equilibrium is E1. As long as production is above the natural level, this process continues, until the econo-my converges to the medium run equilibrium EN, where AD intersects AS at Yn. The price level in the medium run is higher, while the GDP is again equal to Yn. In the transition from E0 to EN, the increase in P reduces the amount of money in real terms, M/P. The resulting excess demand for money leads to an increase in the interest rate that contracts aggregate demand and production. This progressive increase in i ex-plains why output decreases during the transition.

b) The government will have to carry out a reduction of G, that leads immediately to the mediumrun equilibrium EG by moving AD leftward to ADG. Since the production is at the same level at EN and EG, aggregate demand will also be the same in these two equilibria. In particular, consumption demand will be equal at EN and EG (because Y is at the natural level in both equilibria, and taxes are unchanged), while G is smaller at EG (for the fiscal contraction), and investment will therefore be greater at


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EG than at EN. A greater investment requires a lower interest rate at EG (being the output equal). The change in investment between EG and EN is, in absolute value, equal to the change in G in these two equilibria.

Problem Set IMacroeconomicsAcademic Year 2012-2013 BIEMF

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