ECON 301- Chapter 5 Assignment
ou were recently hired to replace the manager of the Roller Division at a major conveyor-manufacturing firm, despite the manager's strong external sales record. Roller manufacturing is relatively simple, requiring only labor and a machine that cuts and crimps rollers. As you begin reviewing the company's production information, you learn that labor is paid $14 per hour and the last worker hired produced 110 rollers per hour. The company rents roller cutters and crimping machines for $18 per hour, and the marginal product of capital is 135 rollers per hour. Should you change the mix of capital and labor, and if so, how should it change?
Given in the question that the last worker hired produces 110 rollers, implying that marginal product of labour is = 110. Price of labour = $14. The optimal condition for hiring workers = MPL/PL. = 110/14 = 7.85 Similarly, the MPK = 135 and Pk = $18. SO the optimal condition is = 135/18 = 7.5 Clearly, MPL/PL > MPK/PK. We know in equilibrium, MPL/PL = MPK/PK, so to get to that situation, starting where MPL/PL > MPK/PK, if the manager changes the product mix, such that manager now chooses more of labour and less of capital, the output production can increase. So option C is correct.
According to The Wall Street Journal, Mitsubishi Motors recently announced a major restructuring plan in an attempt to reverse declining global sales. Suppose that as part of the restructuring plan Mitsubishi conducts an analysis of how labor and capital are used in its production process. Prior to restructuring Mitsubishi's marginal rate of technical substitution is 0.16 (in absolute value). To hire workers, suppose that Mitsubishi must pay the competitive hourly wage of ¥1,630. In the study of its production process and markets where capital is procured, suppose that Mitsubishi determines that its marginal productivity of capital is 0.6 small cars per hour at its new targeted level of output and that capital is procured in a highly competitive market. The same study indicates that the average selling price of Mitsubishi's smallest car is ¥1,300,000. Determine the rate at which Mitsubishi can rent capital and the marginal productivity of labor at its new targeted level of output. Instruction: Enter your response for marginal productivity of labor rounded to four decimal places. Rental rate of capital: ¥ Marginal productivity of labor: To minimize costs Mitsubishi should hire capital and labor until the marginal rate of technical substitution reaches what proportion? Instruction: Enter your response rounded to four decimal places. -
Given that the marginal rate of technical substitution previously is 0.16 The wage =1630 Marginal productivity of capital (MPK)=.60 small cars The selling price of small cars=1300000 We know that Rental rate of capital=Price of the car* Marginal productivity of capital=1300000*0.60=780,000 Similarly, Wage= Price of the car* Marginal productivity of labour(MPL) This means that 1630=1300000*MPL So MPL=16300/1300000= 0.00125 To minimize costs Mitsubishi should hire capital and labor where the marginal rate of technical substitution = MPL/MPK=0.00125/0.60=0.00208
A multiproduct firm's cost function was recently estimated as: C(Q1,Q2) = 90 - 0.5Q1Q2 +0.4Q12 + 0.3Q22 a. Are there economies of scope in producing 10 units of product 1 and 10 units of product 2? a. No - there are no economies of scope. b. You cannot determine if there are economies of scope. c. Yes - there are economies of scope. b. Are there cost complementarities in producing products 1 and 2? a. You cannot determine if there are cost complementarities. b. Yes - there are cost complementarities. c. No - there are no cost complementarities. c. Suppose the division selling product 2 is floundering and another company has made an offer to buy the exclusive rights to produce product 2. How would the sale of the rights to produce product 2 change the firm's marginal cost of producing product 1? a. Marginal cost would decrease. b. Marginal cost would not change. c. Marginal cost would increase.
Question a). Answer :- Yes - there are economies of scope. Question b). Answer :- Yes- there are cost complementarities. Question c). Answer :- Marginal cost would increase.
A manager hires labor and rents capital equipment in a very competitive market. Currently the wage rate is $12 per hour and capital is rented at $9 per hour. If the marginal product of labor is 40 units of output per hour and the marginal product of capital is 55 units of output per hour, should the firm increase, decrease, or leave unchanged the amount of capital used in its production process?
The firm should increase the amount of capital used the in its production process because as comparing both the prices of labor and capital, the capital is cheaper than labor and the marginal product of capital is 55 units of output per hour which is more than marginal product of labor.Hence, if firm increases the amount of capital used in its production process its production is increase as comparing to increase in amount of labor.
a firm produces output according to a production function: q = f(k,l) = min {3k,3l}. a. how ... Question: A firm produces output according to a production function: Q = F(K,L) = min {3K,3L}. a. How muc... A firm produces output according to a production function: Q = F(K,L) = min {3K,3L}. a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $40 per hour and the rental rate on capital is $25 per hour, what is the cost-minimizing input mix for producing 6 units of output? Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $25 per hour but the rental rate on capital remains at $25 per hour? -Capital increases and labor decreases. -Capital and labor increase. -Capital decreases and labor increases. -It does not change.
a) We are given Q = F(K,L) = min {3K,3L} So if K = 2 and L =3 we have min {3(2),3(3)} thus min {6,9} and Q = 6 b) To produce Q =6 we need to buy at least 2 units of K and L so min (3K,3L) gives 6 . If the wage rate is $40 per hour and the rental rate on capital is $25 per hour, then the cost-minimizing input mix for producing 6 units of output will be 2 units of K and 2 units of L C) It does not change as it is min function where good are used in fixed proportion.