Question

Managers of the Brennan Company used regression analysis to obtain the following estimate

of the demand function for its product:

log Q =2 -1.2 log P + 1.5 log I

where Q is quantity demanded, P is price, and I is consumers’ disposable income.

a.Brennan’s president is considering a 5% price reduction. He argues that these results indicate

that such action will result in a 6% increase in the number of units sold by the firm. Do you

agree? Why or why not?

b. The firm’s treasurer calculates that the p-value that the t statistic of log P is as large (in

absolute value) as it is, given that log P has no realeffect on log Q, is about 0.5. He says that the

estimate of the price elasticityis unreliable. Do you agree? Why or why not?

Answer 1

a) AGREE

given the regression

log Q = 2 -1.2 log P +1.5 Log I

if we take partial derivative of log Q with respect to P we get,

(1/Q) )dQ/dP) = -1.2 (1/P)

the above can be simplied as (P/Q) (dQ/dP) = -1.2

(P/Q) (dQ/dP) is nothing but price elasticity of demand.

Therefore in the above regression estimate, 1.2 is estimate of price elasticity of demand of the commodity.

price elasticity measures the percentage in quantity demanded of a commodity for 1% change in price in its price which is 1.2 here. so for 5% decrease in price quantity demanded will increase by (1.2 multiplied by 5 = ) 6% times.

Hence Brennan's president is correct in interpreting the impact of decrease in price on quantity demanded of the commodity.

b) AGREE

null hypothesis is : log P has no real effect on log Q

The calculated t statistic is so large that the probability of getting such a t statistic (value) is 0.5. This means that if we reject reject the null hypothesis on the basis of t statistic ,we will be wrong 50 times out of 100 times. i.e probability of TYPE I error is 0.5. therefore we cannot reject the statement that : log P has no real effect on Log Q.

And if log P has no real effect on log Q then estimate of elasticity is unreliable as argued by the firm's treasurer.