Problem #1
Based on the best available econometric estimates, the market elasticity of demand for your firm’s product is -1.50. The marginal cost of producing the product is constant at $100, while average total cost at current production levels is $200. Determine your optimal per unit price if:
a. You are a monopolist.
P = (-1.5/(1-1.5))*100=300
b. You compete against one other firm in a Cournot oligopoly.
P = ((2)*(-1.5))/(1+(2)(-1.5))*100=150
c. You compete against 19 other firms in a Cournot oligopoly.
P = ((19)*(-1.5))/(1+(19)(-1.5))*100=103.73
Problem #2
You are a manager of a monopoly that sells a product to two groups of consumers in different parts of the country. Group 1’s elasticity of demand is -2, while group 2’s is -6. Your marginal cost of producing the product is $10.
a. Determine your optimal markups and prices under third-degree price discrimination.
G1(1-2/-2)=10 = (-1/-2)=10 = 20
G2(1-6/-6)= 10 = (-5/-6)=10 = 12
b. Identify the conditions under which third-degree price discrimination enhances profits.
- The firm must have some means of identifying the elasticity of demand by different groups of consumers.
- No type of price discrimination will work if the consumers purchasing at lower prices can resell their purchases to individuals being charged higher prices.
Problem #3
You are the manager of a monopoly. A typical consumer’s inverse demand function for your firm’s product is P = 100 – 20Q, and your cost function is C(Q) = 20Q.
P=100-20Q
Q=5-0.05P
MR=100-40Q
MC=20
a. Determine the optimal two-part pricing strategy.
1/2(100-20(5-1)
½[(100-80)20]=200
b. How...