Question

Assume you are the manager of Wenstrom Brewing Company (WBC) and you face the following demand for your beer: QWBC = 12 - 3PWBC + 4PPBR. Suppose you sell your beer for $3.00 per bottle and PBR sells for $1.50 per bottle.

a. Is PBR a substitute or a complement? Explain. b. Calculate the cross-price elasticity of demand between WBC and PBR at the given prices. c. If you want to increase the level of beer you sell by 15%, how much should you change the price? Is this a good idea? Explain. d. Does your answer to part c change if the price of WBC were $2.50 per bottle? Explain. e. If advertising was included in the demand equation and the advertising elasticity was calculated to be 2, how much would consumption of your beer change if you increased the level of advertising by 4%?

Answer 1

Given

QWBC=12-3PWBC+4PPBR

PWBC=$3

PPBR=$1.50

a)

Coefficient of PPBR is positive, it means that PBR is a substitute.

b)

QWBC=12-3PWBC+4PPBR

First we calculate QWBC at given prices

QWBC=12-3*3+4*1.50=9 units

Differentiate QWBC by dPPBR, we get

dQWBC/dPPBR=4

Cross price elasticity of demand=(dQWBC/dPPBR)*(PPBR/QWBC)=4*(1.50/9)=0.67

c)

We need to calculate own price elasticity of demand for estimating the change in price for a given change in quantity demanded.

Differentiate QWBC with respect to PWBC, we get

dQWBC/dPWBC=-3

Own price elasticity of demand=(dQWBC/dPWBC)*(PWBC/QWBC)=-3*(3/9)=-1

If required change in quantity demanded=15%

Needed change in price=Required change in quantity demanded/Own price elasticity of demand

Needed change in price=15%/(-1)=-15%

Price should be decreased by 15%

We can see that demand is unitary elastic at this point. So, Total revenue will remain the the same after price decrease. So, it is not a good idea to increase sales at this point.

d)

QWBC=12-3PWBC+4PPBR

First we calculate QWBC at given prices

QWBC=12-3*2.50+4*1.50=10.50 units

Own price elasticity of demand=(dQWBC/dPWBC)*(PWBC/QWBC)=-3*(2.50/10.50)=-0.71

If required change in quantity demanded=15%

Needed change in price=Required change in quantity demanded/Own price elasticity of demand

Needed change in price=15%/(-0.71)=-21%

Price should be decreased by 21%

Total Revenue will decrease in this case. So, its not a good idea to decrease price at this level also.

e)

Given advertising elasticity of demand=2

Change in consumption=Advertising elasticity of demand*Change in advertising level

Change in consumption=2*4%=8%

Consumption will increase by 8%