14. Suppose Fiberboard Inc. has estimated its log-linear demand function for car

Question

14. Suppose Fiberboard Inc. has estimated its log-linear demand function for cardboard boxes as:

[ln(Boxes)] = 90 – 2.4[ln P] + 1.5[ ln(M)] + 0.3 [ln(Advt)]

Where: Boxes is the quantity of boxes

P is the own price

M is market income

Advt is expenditures on advertising

And: ln denotes the natural logarithm

a. What is the price elasticity of demand?

b. Is advertising expenditures elastic?

c. Assuming each of these variables is statistically significant, how would the consumption of the boxes change if there is a simultaneous 10% reduction in price, a 5% reduction in income, and a 20% reduction in advertising?

Explanation / Answer

a) The slope coefficient in the log-log transformation gives us the elasticity.The price elasticity of demand is equal to the coefficient of ln(P). Therefore elasticity is -2.4.

b) The advertising expenditure is not elastic because the elasticity as given by slope coefficient of ln(Advt) is less than 1.

c) A 10% reduction in price will be followed by a 24% increase in quantity, a 5% reduction in income is followed by 7.5% decrease in consumption and 20% reduction will lead to 6% fall in consumption.

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