Potato farming, like farming of most agricultural products, is highly competitive. Price is determined by demand and supply. Based on U.S. Department of Agriculture statistics, U.S. demand for potatoes is estimated to be Q_(D) = 584 - 20P, where P is the farmer's wholesale price and Q_(D) is consumption of potatoes per capita. One farm i has the following cost function of producing potatoes: C(Q_(i)) = 12 + 7Q_(i) + 3Q_(i)^(2), where Q_(i) is this farm's output level. Assume that farms determine the output level to maximize their own profits and there are n identical potato farms in this market.
You notice that under the pandemic, the market price is $25/unit for potatoes.
Q1.1. Compute the short-run output level per farm, Q_(i), in this market.
Q1.2. Compute the short-run profit per farm in this market.
Q1.3. Compute the short-run farm numbers, n, in this market.
As you have learned in class, this market will reach an equilibrium in the long run. Assume the cost function per farm remains the same.
Q1.4. Compute the long-run output level per farm, Q_(i), in this market.
Q1.5. Compute the long-run market price, P, in this market.
Q1.6. Compute the long-run farm numbers, n, in this market.
Q1.7. After the pandemic, assume the market will gradually shift to the long-run equilibrium. Use a demand-supply curve diagram to explain the changes of farms, market price, and quantity supplied of this shift.
2. Firms A and B make up a cartel that monopolizes the market for a scarce natural resource. The firms' marginal costs are MC_(A) = 6 + 2Q_(A) and MC_(B) = 18 + Q_(B), respectively. They seek to maximize the total profit. The firms have decided to limit their total output to Q = 18.
Q2.1. What outputs should the firms produce to achieve this level of output at minimum total cost?
Q2.2. What is each firm's marginal cost when they limit the total output to Q = 18?
The market demand curve is P = 86 - Q, where Q is the total output of the cartel.
Q2.3. Find Firm A and B's output levels, respectively. (Hint: At the optimum, MR = MC_(A) = MC_(B).)
Q2.4. Find the cartel's optimal price.