The Log-Linear Demand Function for Beckler's Frozen Pizzas Is:
LnQ_X $P _ { X } = \$ 4.00 , P _ { Y } = \$ 3.50 , S = 40 \% , A = \$ 5,000$

Essay

The log-linear demand function for Beckler's Frozen Pizzas is:
lnQ_X = 4 - 3.80 lnP_X + 0.30 lnP_Y + 0.15 lnS + lnA + 1.50 lnI
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 B eckler'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 percent and to increase advertising expenditures by 10 percent. 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 percent and increases advertising expenditures by 10 percent while Beckler's competitor lowers the price of its pizza by 20 percent, what effect will this have on the number of Beckler's pizzas sold per week?