Question

13. Consider a market for homogeneous hamburgers produced in a constant cost competitive industry. Suppose there are 600 Type 1 consumers that each have a utility function of ?1(?, ?) = ?^0.1?^0.9 and 400 Type 2 consumers that each have a utility function of ?2(?, ?) = ?^0.2?^0.8, where x is hamburgers and y is a composite commodity representing the rest of the consumer’s consumption (assume ?? = 1). The income for both types of consumers is $210. Each hamburger producer has the following long-run total cost function: ?(?) = ?^3 − 50?^2 + 632?.

a. What is the long-run competitive equilibrium for hamburgers? Specifically find:

i. What is the long-run competitive market equilibrium price?

ii. What is the quantity produced per firm?

iii. What is the demand function for each Type 1 consumer?

iv. What is the demand function for each Type 2 consumer?

v. How much does each Type 1 consumer purchase?

vi. How much does each Type 2 consumer purchase?

vii. What is the market demand function?

viii. What is the market quantity demanded?

ix. How many firms are there in the market?

b. Now, consider the same market during an economic recession where consumer incomes fall to $140. Now what is the long-run competitive equilibrium for hamburgers? Specifically find:

i. What is the long-run competitive market equilibrium price?

ii. What is the quantity produced per firm?

iii. What is the demand function for each Type 1 consumer?

iv. What is the demand function for each Type 2 consumer?

v. How much does each Type 1 consumer purchase?

vi. How much does each Type 2 consumer purchase?

vii. What is the market demand function?

viii. What is the market quantity demanded?

ix. How many firms are there in the market?

c. Above we considered the market just for hamburgers, but now let’s think in terms of general equilibrium. Use a graph of the Production Possibilities Frontier (PPF) and an Edgeworth box to explain the effects of the recession on hamburgers (x) and all other goods (y). How did it affect the amounts of x and y produced? How did it affect the usage rate of labor and capital in the economy? Finally, relate your answers to the recent Great Recession experienced from 2007-2009 (and the slow recovery period after).

Answer 1

Part (A)

long run equilibrium price for hamburger is $ 7

demad for hamburger by type I consumer
total demand for hamburger by type I consumers	600*3=1800
demand for hamburger by type II consumer
total demand for hamburger by type II consumers	6*400=2400
total quantity of hamburgers sold in the market	1800+2400=4200

Part (B)

long run competitive price will remain at $ 7

demad for hamburger by type I consumer
total demand for hamburger by type I consumers	600*2=1200
demand for hamburger by type II consumer
total demand for hamburger by type II consumers	4*400=1600
total quantity of hamburgers sold in the market	1200+1600=2800

Part (C)

Recession will shift the production possibility frontier inwards leading to a lower production of hamburger and composite good. This will lead to lower employment of labor and capital. Recession also leads to fall in incomes which shift consumers to an indifference curve with lower utility thereby reducing consumption of both the goods hamburgers and composite good