Question

The log-log demand function for Beckler's Frozen Pizzas is: lnQX = 4 – 0.70 lnPX - 0.50 lnPY + 1.5 lnS + 1.2lnA + 0.40 lnI

The number of pizzas sold per week (QX) depends on the price charged for a pizza (PX), the price charged for a cheese sticks (PY), the percentage of single-parent families (S), monthly advertising expenditures (A) in thousands, and average annual household income (I) in thousands. Answer the following questions by filling in the table below:

i. Interpret the own-price elasticity and indicate whether it is elastic.

ii. Determine the cross-price elasticity in the estimated equation and interpret it.

iii. What does the income elasticity say about Beckler’s Frozen pizza?

iv. What will be the percentage change in the number of pizzas sold if A increases by 5.0%?

v. Indicate whether Qx is elastic or inelastic with respect to single-parent families (S). And why?

vi. The manager of Beckler's plans to increase its price by 5%. How will you advise him, and why?

Answer 1

Solution: We have the demand function lnQX = 4 – 0.70 lnPX - 0.50 lnPY + 1.5 lnS + 1.2lnA + 0.40 lnI

a) Own price elasticity of demand = -0.70. This is inelastic because absolute value is less than one.

b) Cross price elasticity of demand is -0.50 and this shows that a 1 percent rise in price of Y would reduce the quantity demanded of X by 0.5 percent.

c) Income elasticity is 0.40 which is positive. Hence pizzas are normal good because a rise in income will increase the quantity demanded of pizzas

d) Advertising elasticity is 1.2. When there is an increase in advertising expenditure by 5%, quantity of pizzas demanded rises by 1.2*5% = 6 percent

e) The single-parent-families elasticity of demand is 1.5 and it greater than 0. This implies that the demand is elastic

f) We would recommend such price increase because the own price elasticity is 0.70 making demand inelastic. This raises revenue because when demand is inelastic, price rise increases revenue.