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Firm-Level Implications of Demand Fluctuations

Using Regression Results in Decision Making:

Advertising Mix, Interest Subsidies and Pricing Policies

Forecasting Demand and Inventory Management

Business Cycle Aspects

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Choosing Price and Advertising

• QD = B0 (Price)b1 (ADV)b2

• LogQD = b0 + b1 LogPRICE + b2 LogADV

• Here b1 and b2 are elasticities.

• Reasonable to expect: b1 < -1 , 0 < b2 < 1 :

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ElasticitiesLogQD = b0 + b1 LogPRICE + b2 LogADV

If Price rises by 1% then QD will rise by b1%

Clearly b1 < 0. Say b1 = - 0.5: firm will keep raising price forever -> price rises by 1%, quantity falls by 0.5%, so revenue rises, but costs fall. Need b1 < -1.

Clearly b2 > 0 . Say b2 > 1: ADV up by 1% raises demand by more than 1%. If marginal production costs are not increasing, the firm will keep increasing ADV. So 0 < b2 < 1 reasonable.

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Profit Maximization

Firm chooses PRICE and ADV to Max. Profit.

Profit = Revenue - Cost

Revenue = PRICE x QD

Cost = CAVC x QD + FC + PRADV x ADV

CAVC = constant average variable cost, FC = fixed cost, PRADV = price of advertising.

Note that we ignore inventories and that all demand is assumed to lead to sales.

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Optimal Price

PRICE = [b1 / (1+b1)] x CAVC

Price is set as markup above average variable cost.

Say b1 = - 2 in regression, then Optimal Price = 2 times CACV

The more competitive the industry the more negative will be b1. In perfect competition b1 = - infinity -> PRICE = CACV

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Advertising Mix

LogQD = b0 + b1LogPRICE + b2LogADVNP + b3LogADVTV

Cost: PRICENP x ADVNP + PRICETV x ADVTV

Say you adjust advertising mix by raising NP and lowering TV advertising, keeping cost constant:

PRICENP x ADVNP + PRICETV x ADVTV = 0

ADVNP / ADVTP = - PRICETV / PRICENP

When is the resulting % change in QD positive? :

b2 % ADVNP > - b3 % ADVTV, or:

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b2 ( ADVNP/ADVNP) > - b3 ( ADVTV/ADVTV)

Since ADVNP/ADVTV = - PRICETV / PRICENP

ADVTV/ADVNP > (b3/ b2) (PRICENP/PRICETV).

Thus, if the above holds, you will increase QD keeping costs the same as long as you raise ADVNP while lowering ADVTV. You should keep doing so until you no longer benefit. At that point:

ADVTV/ADVNP = (b3 / b2) (PRICENP/PRICETV)

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Example ProblemLogQD = 20 - 3 LogPRICE +

0.4 LogADVNP + 0.8 LogADVTV

FC = 10, CAVC = 12, PRICENP = 3 per ad, PRICETV = 30 per ad.

Find the optimal Price and Marketing Mix:

PRICE = 1.5 x 12 = 18

ADVTV/ADVNP = (0.8 / 0.4) (3/30) = 0.20

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Rebate or Interest Subsidy?QD = a0 + a1 PRICE + a2 REBATE + a3 ISUB

Expect: a3 > 0 , a1 - a2 (?)

Cost: [REBATE + ISUB (PRICE-REBATE-DOWNPAY)] x QD

Increase rebate while lowering interest subsidy, keeping QD constant:

REBATE / ISUB = - a3 / a2

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REBATE / ISUB = - a3 / a2

What is the change in Cost?

[REBATE + ISUB (PRICE-REBATE-DOWNPAY)] x QD

Cost = [ REBATE (1 - ISUB) + ISUB (PRICE-REBATE - DOWNPAY)]QD < 0 ?

Using the equation at the top of the page:

PRICE - REBATE - DOWNPAY > (a3 / a2)(1 - ISUB) ?

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Thus, you can lower your cost by increasing your Rebate and decreasing your Interest Subsidy, leaving demand unchanged, until the equation holds with equality:

PRICE - REBATE - DOWNPAY = (a3 / a2)(1 - ISUB)

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We have looked at the use of regression results for making Pricing and Marketing Mix decisions.

Next we will consider how regression results can be used to forecast demand which will help make Production and Inventory decisions

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Motives for Holding Inventory • Bufferstock -- if costs of stocking out

exceed inventory holding costs. [for materials, if supply interruptions may occur]

• Production Smoothing -- often a relatively stable level of production is less costly, so in times of low demand you may be best off producing for inventory to stabilize production. [for materials, transport may be cheaper]

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Cost

Production

Q1 Q2Q1 + Q2

2

C(Q2)

C(Q1)

C(Q)

C(Q)

Production Smoothing

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More motives for holding inventory:

• Production Bunching -- in industries with high start-up you may be best off producing high volume (exceeding current demand) when you do produce. [for materials, if ordering costs are high]

• Speculation -- holding inventory because you expect your product to appreciate in value. [for materials, you may expect suppliers to raise prices].

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Costs of Holding Inventory

• Storage (warehouse space, surveillance, upkeep, transportation)

• Interest foregone (real interest only)

• Insurance (or risk disaster: fire, flood, etc)

• Theft (employees or others)

• Depreciation (nature or fashion)

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Value of Forecasting Demand

• Better forecasts reduce demand uncertainty, decreasing the need for bufferstocks.

• Forecasts of future demand help firms smooth production, lowering average production costs.

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Automobile Industry and Inventory

Production Smoothing and Bufferstock motives for finished goods.

Bufferstock and Bunching motives for materials.

Significant: storage costs, interest loss, depreciation.

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Trends:

Recently, decreases in inventory-to-sales ratios. More so in intermediate stages of production than in final goods.

Reasons: improvements in transportation (deregulation, competition) and communication, bar-coding and computerization.

Just-In-Time inventory policy: fashionable, lowers inventory costs but exposes firms to interruptions, forecasting becomes crucial.

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Inventories and the Business CycleInvt+1 = Invt + Prodt - Salest

Invt+1 = Invt + (Prodt - DemandForecastt) - DemandShockt

Invt+1 - Invt = PlannedInvt + UnplannedInvt

Planned inventory increases signal a business cyle upturn, Unplanned increases signal a downturn. Inventory-to-sales ratios are procyclical in U.S. data, suggesting most inventory increases are planned.

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• Unplanned inventory increases cause firms to produce less in the future, which lowers future incomes and future demand. As a result, one-time negative demand shocks have persistent effects on the economy. These effects are sometimes described as inventory cycles.

• Inventory changes during the business cycle are on average larger than changes in GDP over the cycle (Table 1, Allen article).

• Reductions in inventory-to-sales ratios have not decreased the amplitude of business cycles.

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Differences in Manufacturing vs. Services Demand Volatility

• No pent-up demand for services. Manufactured goods purchases may be deferred until one can better afford them, accentuating recessions.

• No inventory build-up in service sector. So less susceptible to inventory cycles.

• Few services are tradable internationally, so not subject to exchange rate fluctuations

• Services typically do not require much capital so not subject to interest rate fluctuations.

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Chart 2 in Filardo article shows the dramatic differences in employment variability between the service sector and the recession-prone manufacturing sector.

The shift over time in employment from manufacturing to services (shown in Chart 1), however, has had little effect on the amplitude of the business cycle (as shown in Chart 3). Reasons: the output share of the manufacturing sector has barely changed; outsources by manufacturing firms now counts as services what used to be counted as manufacturing; services have become more cyclical.