A monopolist sells its good in the US and French markets. The US inverse demand

Question

A monopolist sells its good in the US and French markets. The US inverse demand function is P_US = 20 - Qus and the French inverse demand function is P_F = 18 -.25 Q_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_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 arc 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 does 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 cost curves. What price should it set for the two groups to minimize deadweight loss

Explanation / Answer

In order to answer this question you must first identify what quantity the firm will produce. The firm still wants to produce the profit maximizing quantity which is the quantity where MR equals MC. But, the firm’s MR curve is now the same as the firm’s demand curve. So,Q=4.

To calculate the firm’s profit we need to calculate the firm’s TR and the firm’s TC. The firm’s TR is a bit hard to calculate: it is the sum of an area of a triangle plus the area of a rectangle or the area that is underneath the demand curve from a quantity of 0 units to a quantity of 4 units. Thus, TR = (1/2)($20 per unit - $16 per unit)(4 units) + ($16 per unit)(4 units) = $72. The firm’s TC is equal to TC = 36. Thus, the firm’s profit is equal to 36 .

With perfect price discrimination CS is equal to zero since the monopoly is able to capture all of the consumer surplus with its pricing policy

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