Discussion:
1. Over the past decade medical costs have increased more rapidly than other prices. In order to illustrate how rising medical costs have affected consumer alternatives, let X represent the quantity of medical services, and let Y represent the quantity of other goods. Furthermore, let income (I) be measured in hundreds of dollars, the price of medical services and other goods in terms of dollars per minute, with , , and .
a. Graph the budget line, and determine the market rate of substitution.
b. Explain and illustrate the budget line and opportunity set.
c. Show in your graph what happens to the budget constraint if increases to $10.
d. What is the meaning of the slope of the two budget constraints?
(NOTE: Label all graphs)
2. Suppose you are an aide to a U.S. Senator who is concerned about the impact of a recently proposed excise tax on the welfare of her constituents. You explained to the Senator that one way of measuring the impact on her constituents is to determine how the tax change affects the level of consumer surplus enjoyed by the constituents. Based on your arguments, you are given the go-ahead to conduct a formal analysis, and obtain the following estimates of demand and supply: and .
a. Graph the supply and demand curves.
b. What are the equilibrium quantity and equilibrium price?
c. If a $2 excise tax is levied on this good, what will happen to the equilibrium price and quantity? Explain how the tax change affects the level of consumer surplus enjoyed by the constituents.
3. You work for an unemployment agency that distributes unemployment checks to unemployed workers in your state. Your boss recently learned that the President proposed a 21 percent increase in the minimum wage, and wants you to provide her with an estimate of the number of additional workers who will file for unemployment compensation claims next year if the bill passes. Based on library research at a nearby university, you learn that about 200,000 workers in your state earn at or below the current minimum wage. Further library research turns up a study that reports the own price elasticity of demand for minimum wage earners to be (-0.30). Based on your findings, how many additional workers do you think will file unemployment claims in your state?
4. AMS recently instituted an in-house recycling program. The benefits of this program include not only the benefits to the environment of recycling but also the goodwill generated by AMS's leadership in this area. The costs of recycling include all of the energy, labor, and space required to do the recycling. Suppose these benefits and costs are given by TR(Q)=100Q - 2Q2 and TC(Q) = 2Q (Note that MR = 100 - 4Q , and MC= 2 ).
a. What level of Q maximizes the profit of recycling?
b. What is marginal revenue at this level of Q?
c. What is marginal cost at this level of Q?
d. What level of Q minimizes the total costs of recycling?
e. What level of recycling is optimal? Why?
5. The manager of a meat-packing plant can use either butchers (labor) or meat saws (capital) to prepare packages of sirloin steak. Based on estimates provided by an efficiency expert, the firm's production function for sirloin steak is given by Q=K+L.
a. Graph the linear production function corresponding to 5 units of output.
b. What is the marginal product of capital and labor? Does the answer depend on how much labor and capital are used?
c. If the price of labor is $2 per hour and the rental price of capital is $3 per hour, how much capital and labor should be used to minimize the cost of production?
6. Suppose the production function of PowerGuns Co. is given by
Q = 100LK
where Q is the quantity of guns produced in the month, L is the number of workers employed, and K is the number of machines used in the production. The monthly wage rate is $2,500 per worker and the monthly rental rate for a machine is $5,000. Currently PowerGuns
Co. employs 20 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.