1. (a) An electronic firm’s production function is Q = 5LK, where Q = output, L is the amount of labor it uses per period, and K is the amount of capital it uses per period. The price of labor is $1 per unit of labor, and the price of capital is $2 per unit of capital.
Marginal product of labor is 5K
Marginal product of capital is 5L
If the firm wants to produce 20 units of output and does so with 2 units of labor and 2 units of capital, is it using the cost minimizing quantity of labor and capital? If not, what should it do (more labor and less capital or more capital and less labor)? You may assume that fractional quantities of labor and capital are available and can be used (for example the firm can hire 1.5 workers or 2.4 units of capital). Please explain and show all calculations.
2. In the above figure, labor costs $100 per unit. The manager wants to produce 2,500 units of output. You may assume that all the isocost lines shown in the above graph are parallel to each other. Answer the following questions:
(a) At point A is the slope of the isocost line greater than or less than the slope of the isoquant?
(b) What is the total cost of producing 2,500 units of output at point A? Please show your
calculations.
(c) What is the price of capital at point A? Please explain.
(d) When the firm moves from A to B on the isoquant, what happens to the quantity of labor and
the quantity of capital used?
(e) When the firm moves from A to B what happens to the output of the firm? Please explain.
(f) What is the total cost of producing at point B? Please show your calculation.
(g) What is the slope of the budget line at point C? Please explain.
(h) What is the slope of the isoquant at point C? Please explain.
(i) If the firm wishes to produce 2,500 units of output, please explain why the firm will not
choose to produce at point E on the graph. You must give an explanation.
3 (a) Assume that your car has problems with the transmission, and you take it to a mechanic. Is there a principal -agent problem between you and the mechanic? Please give an explanation.
(b) If you hire a real estate agent to sell your house, is there a principal agent problem between you and the real estate agent? Please explain.
6. (a) In a perfectly competitive industry, the market determined price is $12. For a firm cu
ently producing 50 units of output, marginal cost is $15, average total cost is $14, and average variable cost is $7. Is the firm producing the profit maximizing quantity of output? Why or why not? If not, should the firm increase or decrease output to increase profit? Please explain.
(b) The Mercedes Benz dealer in San Francisco states on its website that the same family has owned and operated the company in the same location for over 50 years. It has also claimed in its advertising that it has lower overhead costs than other nea
y auto dealers because it has owned this land for 50 years, and that it charges a lower price for its cars because of its lower overhead. What sort of market, perfectly competitive or monopolistically competitive, is the dealer likely operating in? Please give an explanation based on the information in this question.