Problem 1. Consider a perfectly competitive firm producing watches. Suppose that the firm’s marginal cost of production is 2Q, where Q is the level of output. The fixed cost of production is $100. The total cost is given by C = Q2 + 100.
a. If the price of watches is $60, how many watches should the firm produce to maximize profit?
b. What will the total profit be?
c. At what minimum price will the firm produce a positive output?
d. Derive the individual supply curve. Suppose there are 100 identical firms in the market. Draw the industry supply curve, and derive the equation of the industry supply curve. If the market demand function is given by P = 510 - Q, what will the equilibrium price and quantity be?
e. Suppose the fixed cost of production increases from $100 to $120, and then to $150. What will happen to the firm’s output choice and profit?
Problem 2. The accompanying table below lists three supply points for an individual, perfectly competitive firm operating in the short run.
Price Quantity
$5 15
8 32
10 40
If the industry is composed of 120 identical firms, which of the following will be a point on the short-run industry supply curve?
A) Price = $5, Quantity = 1,650
B) Price = $1,200, Quantity = 40
C) Price = $960, Quantity = 3,840
D) Price = $10, Quantity = 4,800
Problem 3. The market for corn is perfectly competitive, and an individual corn farmer faces the cost curves shown in the accompanying figure. If the price of a bushel of corn in the market is $14, then the farmer will produce ______ of corn and earn an economic ______ equal to ______.
A) 4 bushels; profit; $0.
B) 4 bushels; profit; just less than $80 per bushel
C) 2 bushels; profit; $0
D) 2 bushels; loss; just more than $80 per bushel.
Problem 4. In the accompanying figure, if the price is P1, then the firm earns:
A) a loss equal to (ba) x Q1.
B) a loss equal to (ca) x Q1.
C) a loss equal to (bc) x Q1.
D) zero.
