A monopolist sells its good in the US and French markets. The US inverse demand
ID: 1200744 • Letter: A
Question
A monopolist sells its good in the US and French markets. The US inverse demand function is P_US = 20 - Q_US and the French inverse demand function is P_F = 18 -.25Q_F where both prices P_US and P_F are measured in dollars. The firm's marginal cost of production is constant at MC = 4 in both countries. If the firm can prevent re-sales, what price will it charge in both markets? Suppose a monopolist's costs are described by the function C(Q) = 4 + 2Q^2 and the monopolist faces a demand curve of Q = 20 - p. Suppose that the firm is able to practice perfect price discrimination. What are the values of output, profit, and consumer surplus? Consider a monopolist facing two customer groups. The first has demand p_1 = 10 - q_1/2 and the second has demand p_2 = 20 - q_2. The firm has marginal cost MC(q) = q, where q = q_1 + q_2 is the total amount sold. Suppose it can separate customers into the two groups (third degree price discrimination), each with its own price per unit. How many units does it sell to each group? At what prices? Suppose instead of MC(q) = q, the firm had exactly 4 units to sell to the two groups (and no costs to worry about; the 4 units are already produced). How should it split the units between the goods? Suppose it could first degree price discriminate and charge the full willingness to pay for every unit. How many units docs it sell to each group? (Back to MC(q) = q = q_1 + q_2.) Suppose a regulator could set one per unit price for everyone and knows the demand and marginal CONI curves. What price should it set for the two groups to minimize deadweight loss?Explanation / Answer
Q=20-P
C(Q)=4 + 2Q^2
COST FUNCTION IS =4 + 2Q(20-P)^2
=4+2(400-P^2)
=4+800-2P^2=804=2P^2=402=P^2
P=20.04
Generate TC & tr
TR=q=20-p
= p=20-q
MR= p=20q-q^2
· Profit Maximisation occurs where MR=MC
· MC=4 + 2Q^2= 4Q
Now, equating
4Q=20-Q
5Q=20
=Q=4 & P=16
To Calculate Profit for A Monopoly
Profit = Total revenue – Total Cost
Total Revenue = 16*4 = 64
Total Cost = 4 * 4 = 16
· Therefore, total profit for this section is = 64-16=48