Ch 11 #1, 2, 4, 6, 7(DW), 12(DW), 18, 21, 22, TW11

Question 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 $75, while average total cost at current production levels is $200. Determine your optimal per unit price if: a. You are a monopolist. b. You compete against one other firm in a Cournot oligopoly. c. You compete against 19 other firms in a Cournot oligopoly.
a. P=(EF/1+EF)*MC
=> (-1.50/-.50) * 75
=> 225
b. P = (NEm/1+NEm)*MC
=> (-1.50/-.50) * 75
=> 225
c. P = (NEm/1+NEm)*MC
=> (19* -1.50/1+ 19*-.50) * 75
=> (-28.5 / -8.5) * 75
=> 251

4.
P1= (E1/1+ E1)MC = (-2/1-2)10 = $20 and the optimal markup is 2.
P2= (E2/1+ E2)MC = (-6/1-6)10 = $60 and the optimal markup is 6.

b. Profit maximization should follow the next condition: MR1= MR2 => P1(1+ E1/ E1) = P2(1+ E2/ E2). Groups of consumers are already identified as well as their elasticity of demands. Therefore, in order to enhance profits, there must be differences in the elasticity of demand of the different consumers. Since Group 2 has a more elastic demand for the product than do Group 1, they should be charged a lower price to maximize profits. In addition, the manager should prevent resell the product as consumers buying at lower price can resell their purchases to the group paying higher price.

6.

a. The inverse function is P = 200 – 4Q and the Marginal cost is $120.
The optimal number of units in a package is that output where price equals marginal cost. Therefor we set 200 – 4Q = 120 and we get, Q = 20 units.

b. The total value to a consumer of the 20 units, which is $3,200
(.5)(20)($200 - $120) + ($120)(20) = $3,200

7. You are the manager of a firm that produces products X and Y at zero cost. You know that different types of