Second Take Home Exam
· Spend no more than 3 hours working on the exam.
· You may use your text, your class notes, and your homework as resources.
· You may NOT collaborate with other students, or use any other resources not listed above.
· You may ask me questions about the exam, which I may or may not answer.
· Turn in the exam no later than the beginning of class on Friday, March 15
Part I: Short Answer—Answer in 2-5 sentences; 5 points each
1. Why does the profit maximizing level of output for a firm occur where MR = MC?
2. What is market power and how does the degree of market power a firm has influence the demand curve that the firm faces?
3. Define an isoquant. What is the economic significance of its slope?
4. Describe the differences among increasing, decreasing, and constant returns to scale production functions.
5. What is the relationship between marginal productivity and marginal cost?
6. Explain the relationship between a perfectly competitive firm's MC curve, AVC curve, and supply curve.
Part II: Graphs/Problems—10 points each; show all your work for full credit.
1. Frisbees are produced according to the production function:
Q = 2K + L
a. If K = 10, how much labor is needed to produce 100 Frisbees?
b. If K = 25, how much labor is needed to porduce 100 Frisbees?
c. What is the Rate of Technical Substitution in this production function?
d. Graph, in very general terms, the isoquant for 100 Frisbees.
e. What does the shape of this isoquant suggest about the technology used to produce frisbees?
2. Present the graphic depictions of a perfectly competitive firm at its breakeven level of production, a loss minimizing level of production, and a profit maximizing level of production. Clearly label all graphs.
3. Trapper Joe, the fur trader, has found that his production function in acquiring pelts is given by
Q = 2√H
where Q = the number of pelts acquired in a day
H = the number of hours Joe's employees spend hunting and trapping in one day
Joe pays his employees $8 an hour
a. Calculate Joe's total and average cost curves (as a function of Q)
b. What is Joe's total cost of the day if he acquires four pelts? Six pelts? Eight pelts? What is his average costs per pelt for the day if he acquires four pelts? Six pelts? Eight pelts?
4. Universal Widget produces high-quality widgets at its plant in Nevada for sale throughout the world. The cost function for total widget production (q) is given by:
Total costs = 10q
Marginal costs = 10
Widgets are demanded only in Australia (where the demand curve is given by q = 100- 2P and MR = 50 -q) and Lapland (where the demand curve is given by q = 120 -4P and MR = 30-q/2). If Universal Widget can control the quantities supplied to each market, how many should it sell in each location in order to maximize total profits? What are these profits?
Part II: Longer Answers—Answer in a paragraph or so; 10 points each
1. It can be argued that production analysis using isoquants and isocost functions is analogous to consumer analysis using indifference curves and budget lines. Describe as many points of commonality between the two analyses as you can.
2. Perfectly competitive firms face very different decisions in the Short Run and the Long Run. Why? Describe as many points of difference as possible, explaining why these differences arise.
3. What role does technology play in a firm's production decisions? In what ways does technology act as a constraint?