1. Suppose that you can sell as much of a product as you want at $100 per unit. Your marginal cost is: MC=2Q. Your fixed cost is $50. What is the optimal output level? What is the optimal output if your fixed cost is $60?
2. Prior to a price increase, the price and quantity demanded for a product were $10 and 100 respectively. After the price increase, they were $12 and 90.
a. Calculate the arc elasticity demand.
b. Is the demand elastic or inelastic over this region?
c. What happened to total revenue?
3. Assume that demand for Product A can be expressed QA=500-5PA+3PB and demand for Product B can be expressed as QB=300-2PB+PA. Currently, market prices and quantities for these goods are PA=5, PB=2, QA=481, and QB=301.
a. Suppose the price of Product B increases to 3. What happens to the quantity demanded of both products?
b. Calculate the arc cross elasticity between product A and product B using prices for product B of 2 and 3.
c. Are these goods substitutes or complements?
4. The Zenvox Television Company faces a demand function for its products that can be expressed as Q=4000-P+.5I, where Q is the number of televisions, P is the price per television, and I is average monthly income. Average monthly income is currently equal to $2,000. Answer following questions.
a. Graph the demand curve faced by Zenvox at the current income level. On same graph depict Marginal revenue. At what price and quantity is Zenvox’s total revenue maximized? What is the marginal revenue at this point? Show calculations.
b. What is the price elasticity of Zenvox’s demand function at the price and quantity derived in part (a)? What does value mean in words?
c. Why might Zenvox choose to produce at a price and quantity different than that derived in part (a)?
5. Suppose that the price of product A falls from $20 to $15. In response, the quantity demanded of an increase from 100 to 120 units. The quantity demanded for product B increases from 200 to 300 units. Calculate the arc cross elasticity between Product B and Product A. Is B a substitute or complement for A? Why? Does Product A follow the “law of demand”? Why?
Q TC TFC TVC MC AC AFC AVC
1 500 80
a. Complete table.
b. Graph TC, TFC, TVC, MC, AC, AFC, and AVC against Q.
7. Suppose the production function of PowerGuns Co. is given by Q=25LK, where Q is the quantity of guns produced in a month, L is the number of workers employed, and K is the number of machines used in the production. The monthly wage rate is $3000 per worker and the monthly rental rate for a machine is $6000. Currently PowerGuns Co employs 25 workers and 40 machines. Assume perfect divisibility of labor and machines.
a. What is the current average product of labor for PowerGuns Co? What is the current marginal product of Machines? (assume 1 unit increase in machines)
b. Does PowerGuns production function display increasing, decreasing or constant returns to scale? Explain.
c. What is the total cost of the current production of PowerGuns in a month? What is the average cost to produce a shooting gun? Assuming the number of machines does not change, what is the marginal cost of producing one additional gun?
d. What is the law of diminishing returns? Does this production display this characteristic? Explain.
8. A Michigan court ruled in the 1990’s that General Motors did not have the right to close a particular Michigan plant and lay people off. Do you think this ruling benefited the people of Michigan? Explain.
9. The Suji Corp. has a monopoly in a particular chemical market. The industry demand curve is P=1,000-5Q. Marginal Cost is 3Q. What is Suji’s profit-maximizing output and price? Calculate the corresponding profits.
10. Assume the industry demand for a product is P=1,000-20Q. Assume that the marginal cost of product is $10 per unit.
a. What price and output will occur under pure competition? What price and output will occur under a pure monopoly (assume one price is charged to all customers)?
b. Draw a graph that shows the lost gains from trade that result from having a monopoly.