Frances sells earrings in the perfectly competitive earring market. Her output p

Question

Frances sells earrings in the perfectly competitive earring market. Her output per day and costs are as follows:
OUTPUT PER DAY TOTAL COST
0 1
1 2.5
2 3.5
3 4.2
4 4.5
5 5.2
6 6.8
7 8.7
8 10.7
9 13
a) If the current equilibrium price in the earring market is $1.8, how many earrings will Frances produce, what price will she charge, and how much profit (or loss) will she make?
b) Suppose the equilibrium price of earrings falls to $1. Now how many earrings will Frances produce, what price will she charge, and how much profit (or loss) will she make? Show your work.
c) Suppose the equilibrium price of earrings falls to $0.25. Now how many earrings will Frances produce, what price will she charge, and how much profit (or loss) will she make?

Explanation / Answer

a. Because the market is perfectly competitive, Frances must sell the earrings at the equilibrium price. Since the equilibrium price is $1.8, the number of earrings she will produce will be the highest output of earrings where the cost of producing an additional earring does not exceed the equilibrium price of $1.8. In other words, Frances does not want to sell an earring at a loss. For example, the total cost of producing 1 earring is $2.5 and the total cost of producing 2 earrings is $3.5. The cost of producing the additional earring is $1, however Frances can sell this additional earring for $1.8, making a profit. Therefore, the profit-maximizing output would be 6 earrings because the cost of producing 7 earrings is an additional $1.9 and would be sold at a loss. The profit will be ($1.8 x 6) - $6.8 = $4. b. Again here, Frances will have to sell at the equilibrium price of $1. Using the same method as above, we can conclude that Frances will produce 5 units of output because in this case, Frances is trying to minimize her loss. At any output, Frances will be losing money, but using the method from above, we find that producing the 4th and 5th units of output cost less than $1 and therefore will help minimize the loss. The loss would be ($1 x 5) - $5.2 = -$0.2. c. Again here, Frances will have to sell at the equilibrium price of $0.25. However, using the same method, we see that the cost of producing an additional earring at any output is greater than $0.25, so the loss will only increase at any unit of output. Therefore, Frances will produce 0 units of output in order to minimize the loss. Eventually, the equilibrium price will go back up in the perfectly competitive market because producers cannot afford to sell earrings at this low a price. The loss is ($0.25 x 0) - 1 = -$1.

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