3. (Hint: this problem will be easier if you draw a graph) The demand for peanut

Question

3. (Hint: this problem will be easier if you draw a graph) The demand for peanuts is given by P-305-2Q. I. Initially, the peanut market is perfectly competitive, and each firm has minimum avcrage cost equal to 5 (remember, MC = AC at minimum AC). Ia. Find the competitive price and quantity. Ib. What is each individual firm's profit in competitive equilibrium? Ic. In equilibrium, what is consumer's surplus? IL. One firm buys all of the other peanut firms, obtaining a monopoly in the peanut industry. The monopoly has constant returns to scale and has a constant marginal cost MC 5 (remember, when constant returns to scale. MC Ila. What is the marginal revenue the monopolist faces? ITb. Find the monopoly price and quantity. Call these P and Qa lIc. What is the profit for the monopolist? IId. Find the dead weight welfare loss caused by the monopolization of the peanut industry.

Explanation / Answer

Part I

Demand is P = 305 - 2Q. Min AC = $5. This implies long run price is $5 and so price is $5. Quantity is found to

5 = 305 - 2Q

Q* = 150. Since P = AC there is no economic profit. Consumer surplus = 0.5*(305 - 5)*150 = 22500

Part II

Price is P = 305 - 2Qm and so MR = 305 - 4Qm

Monopoly quantity is Qm where MR = MC

305 - 4Qm = 5

Qm = 75 units. Price Pm = 305 - 150 =$155

Profit = (Pm - AC)Qm = (155 - 5)*75 = 11250

DWL = 0.5*(155 - 5)*(150 - 75) = $5625

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