1. Given the total cost function TC = 1000+10Q, where Q = units of output.
(a) Determine the equations for TFC (total xed cost) and TVC (total variable cost), and illustrate graphically the relationship among TFC,
TVC, and TC.
(b) Determine the equations for AFC (average xed cost), AVC (average variable cost), ATC (average total cost), and MC (marginal cost). Graphically illustrate the relationships to one another.
(c) What, if anything, can you infer about the nature of the underlying production function?
(d) How much is the marginal cost of the 100th unit of output? How much is AVC at an output of 100 units? Explain why MC = AVC at each rate of output.
2. The owner of the Karen's Car Wash believes that the relationship between the number of cars washed and labor is Q = 0.6 + 4L 0.8L2, where Q is the number of cars washed per hour, and L is the number of people employed per hour. The rm receives $4.50 for each car washed, and the hourly wage rate for each person is $3.60. The cost of other inputs like water is trivial, and hence they are ignored.
(a) How many people should be employed to maximize pro t?
(b) What will be the rms hourly pro t?
3. The total cost function of a shirt manufacturer is TC = 10 + 26Q 5Q2 + 0.5Q3, where TC is in hundreds of dollars per month and Q is output in hundreds of shirts per month.
(a) What is the equation for TVC?
(b) What is the equation for AVC?
(c) What is the equation for AFC?
(d) What is the equation for ATC?
(e) What is the equation for MC?
(f) In the above problem, try plotting the curves in excel. Now eyeball where diminishing marginal returns to input set in. (Remember that MC = w=MP). Now solve for the point where diminishing returns sets in.
4. The Deering Manufacturing Companys short-run average cost function in 1996 is AC = 3 + 4Q where AC is the rms average cost (in dollars per pound of the product), and Q is its output rate.
(a) Obtain an equation for the rms short-run total cost function.
(b) Does the rm have any xed costs? Explain.
(c) If the price of the Deering Manufacturing Companys product is $3, is the rm making pro ts or losses? Explain.
(d) Derive an equation for the marginal cost function.
(e) Does this rm show diminishing returns to input? Why?
5. The Wang Corporation produces 1,000 wood cabinets and 500 wood desks per year, the total cost being $30,000. If the rm produced 1,000 wood cabinets only the cost would be $23,000. If the rm produced 500 wood tables only, the cost would be $11,000. Does this show economies of scale or economies of scope? Why?