The Log-Linear Demand Function for Beckler's Frozen Pizzas Is

Essay

The log-linear demand function for Beckler's Frozen Pizzas is:
lnQ_X = 4 - 3.80 ln P_X + 0.30 ln P_Y + 0.15 ln S + ln A + 1.50 ln I
The number of pizzas sold per week (Q_X) depends on the price charged for a pizza (P_X), the price charged for a competitor's brand of pizza (P_Y), the percentage of single parent families (S), monthly advertising expenditures (A) in thousands, and average annual household income (I) in thousands.
(i) If P_X = $4.00, P_Y = $3.50, S = 40%, A = $5,000, and I = $40,000, how many pizzas can Beckler's expect to sell in a week?
(ii) Interpret the price elasticity, cross-price elasticity, family structure elasticity, advertising elasticity, and income elasticity of demand for pizzas.
(iii) The president of Beckler's plans to increase the price of their pizzas by 25% and to increase advertising expenditures by 10%. By what percentage can the number of pizzas sold by Beckler's be expected to change? Will total revenue increase, decrease, or remain the same? Explain your answer.
(iv) If Beckler's lowers the price of its pizzas by 5% and increases advertising expenditures by 10% while Beckler's competitor lowers the price of its pizza by 20%, what effect will this have on the number of Beckler's pizzas sold per week?