Question

Question 1 (36 points) Suppose that the demand function is given as follows: 5000 3Pr +P, -2I and 2P T - P. where Pr denotes price of good x. P, denotes the price of a related product y, I denotes income, T denotes the tax imposed by the government on firms and P. denotes the price of alternative product that can be produced by firms a-) (8 points) Find equilibrium price and output (Peg and Oe") as a function of exogenous variables income (D), price of the related product (P,). tax (T) and price of alternative product that can be produced by firms P b-) (8 points) Using comparative statics, find how equilibrium price and output change as Price of the related product (P) and income (I) change (i.e. find. -. Support your oI findings with graphs. Are goods x and y complements or substitutes? Is good x a normal good or an inferior good? c-)(10 points) Suppose now that exogenous variables are given as follows: Income (1-2000. P,' 200. T-150. P = 150 . Find the equilibrium price and output values. Calculate the price elasticity of demand at the equilibrium? Is total revenue maximized at the equilibrium price? If not, what is the optimal strategy to maximize revenue? Why? d-) (10 points) Find the income elasticity of demand at the equilibrium price and output found in part c Is good x a normal good? Find the cross price elasticity of demand for x with respect to price of v? Are the products complements or substitutes? Are you consistent with part b?

Answer 1

Q^d_x = 5000 - 3 P_x + p_y -2 I Q^s_x = 2 P_x-T -P_z a)at equilibrium Q^alpha_x = Q^s_x rightarrow 5000 -3 P_x + P_y-2 I = 2P_x T P_z rightarrow 5 P^eq_x = 5000 + P_y -2 I + T + P_z rightarrow P^eq_x = 2000 + 2/5 (p_y -2 I) - 3/ 5 (T + P_z) partial differential Q x^eq/ partial differential QP_y = 2 /5 > 0 partial differential Q_x^eq/ 2 I =_4/5 < 0 partial differential P_x^eq/partial differential P_y = 1 /5 > 0 partial differential P_x^eq/partial differential I = -2 /5 < 0 \r\n Since partial differential Q_x^eq/partial differential I < 0 implies it is inferior good Since partial differential Q_x^eq/ partial differential P_y > 0 implies x and y are substitutes I = 2000, P_y