1. A car company's short-run production function is Q=10KL, where Q represents quantity of cars, K denotes capital input (units per hour), and L denotes labor input (units of worker time per hour). The marginal products of labor and capital are as follows:
MPL=10K, MPK=10L
The company can rent its equipment and hire workers at competitive rates. Equipment needed for this operation can be rented at $100 per hour, and labor can be hired at $50 per worker hour. The company has allocated $50,000 for the initial investment.
a. What is the appropriate input mix to get the greatest output?
b. What is the highest level of output the company can achieve with the initial investment?
c. Explain what would happen in the short run to the appropriate input mix if production is increased by more investment. Would the input combination be different in the long run? If so, how would it change? Explain.
2. A firm's total cost function is given by the equation:
TC = 4000 + 5Q + 10Q2.
a. Write an expression for each of the following cost concepts:
Total Fixed Cost
Average Fixed Cost
Total Variable Cost
Average Variable Cost
Average Total Cost
b. Given the marginal cost is MC=5 + 20Q,, determine the quantity that minimizes average total cost.
3. Conigan Box Company produces cardboard boxes that are sold in bundles of 1000 boxes. The market is highly competitive, with boxes currently selling for $100 per thousand. Conigan's total and marginal cost curves are:
TC = 3,000,000 + 0.001Q2
MC = 0.002Q
where Q is measured in thousand box bundles per year.
a. Given the market price, how many bundles of the boxes will the company sell?
b. What is the profit (or loss) from selling this amount?
c. Analyze Conigan's position in terms of the shutdown condition. Should Conigan operate or shut down in the short run?
d. What price does the box bundles need to be at, for Conigan to make a profit?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.