Question 18 Consider a firm that has production function f(L,K)=4L2/3K1/3. What is the expression for this firm’s Marginal Product of labor? MPL(L,K)= 2K2/3/3L2/3. MPL(L,K)= 2K2/3/L1/3. MPL(L,K)= 2K1/3/3L1/3. MPL(L,K)= 5K2/3/3L2/3. MPL(L,K)= 8K1/3/3L1/3.
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Question 18
Consider a firm that has production function f(L,K)=4L2/3K1/3. What is the expression for this firm’s Marginal Product of labor?
MPL(L,K)= 2K2/3/3L2/3.
MPL(L,K)= 2K2/3/L1/3.
MPL(L,K)= 2K1/3/3L1/3.
MPL(L,K)= 5K2/3/3L2/3.
MPL(L,K)= 8K1/3/3L1/3.
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- The following is a production function. 50,000- 45,000- 40,000- Draw a graph of marginal product as a function of labor. 35,000- 30,000- 25,000- Total output (Q) 20,000- 15,000- 10,000 ng 5,000- 0+ 0 200 100 300 Units of labor (L) 400 L Q 1.) Using the line drawing tool, graph the marginal product curve from 0 to 100 units of labor. Label this line 'MP Segment 1" 2.) Using the line drawing tool, graph the marginal product curve from 100 to 300 units of labor. Label this line 'MPS Note: Carefully follow the instructions above and only draw the required objects. Does this graph exhibit diminishing returns? Explain your answer. ○ A. Yes, it does exhibit diminishing returns, because the marginal product of labor decreases. B. No, it does not exhibit diminishing returns, because the marginal product of labor is zero. ○ C. No, it does not exhibit diminishing returns, because the marginal product of labor is increasing. ○ D. Yes, it does exhibit diminishing returns, because the marginal…A firm can manufacture a product according to the production function Q = F(K, L) = K0.5L0.5. (a) What is the average product of labor, APL, when the level of capital is fixed at 36 units and the firm uses 16 units of labor? (b) What is the marginal product of labor, MPL, when capital is fixed at 36 units? (c) Suppose capital is fixed at 36 units. If the firm can sell its output at a price of $100 per unit of output and can hire labor at $40 per unit of labor, how many units of labor should the firm hire in order to maximize profits?Suppose a firm is producing 2,475 units of output by hiring 50 workers (W = $20 per hour) and 25 units of capital (R = $10 per hour). The marginal product of labor and marginal product of capital are 30 and 15, respectively. Is the firm minimizing the cost of producing 2,475 units of output? Explain.
- Assume that a firm has a plant of fixed size and that it can vary its output only by varying the amount of labor it employs. The table below shows the relationships among the amount of labor employed, the output of the firm, the marginal product of labor, and the average product of labor. (a) Assume each unit of labor costs the firm $20. Compute the total cost of labor for each quantity of labor the firm might employ, and enter these figures in the table. (b) Now determine the marginal cost of the firm's product as the firm increases its output. Enter these figures in the table. (c) If labor is the only variable input, the total labor cost and total variable cost are equal. Find the average variable cost of the firm's product. Enter these figures in the table. (d) Describe the relationship between the marginal product of labor and the marginal cost of the firm's product. (e) Describe the relationship between the average product of labor and the average variable cost. Quantity of labor…Question 1 The total cost function of a firm is given by: 2 1 C = q(W}?cv)³ Where q is total output, W and V are unit prices of labour (L) and capital (K) respectively a. Find the conditional input demands for labour (L) and capital (K) b. From your result in (a), derive the underlying production function for Question 2 Consider a firm that produces cars with the following production function: 9 = min(aK, bL) a. Find the Marginal Rate of Technical Substitution of labour for capital for this firm b. If per unit prices of capital (K) and labour (L) are r and w respectively, find the input demand functions for K and L; as well as the long run cost function c. Present your solutions graphically. (Thus, draw the Isoquant and Isocost of this firm) Question 3 You have a car valued at Gh60, 000. You estimate that there is a 0.1 percent chance that your car will be stolen. An insurance company offers you insurance against this eventuality for a premium of Gh800. If you are risk-neutral, should…1.) A firm engaged in the manufacture of RTWS faces the short-run production function Q = 250L - 5L², where L is the number of units of labor and Q is the number of RTWs produced annually. a.) How many units of labor are needed to maximize production output? b.) Find the maximum number of RTWs that can be produced by the firm in a year. c.) Compute the marginal product of the 10th unit of labor. d.) How many RTWS can be produced by the firm in a year if there are 10 units of labor? e.) Compute the marginal product of the 40th unit of labor. f.) How many RTWs can be produced by the firm in a year if there are 40 units of labor? g.) Sketch the graph of the production function.
- 2. A firm uses capital (denoted by K) and labor (denoted by L) to produce hockey sticks. The firm's production function is given by q = 2/KL . In the short run, the firm's amount of capital equipment is fixed at K = 100. The rental rate for capital is $1 per unit and the wage rate is equal %3D to $4. a) Calculate the firm's short-run total cost function. Also, calculate the short-run average cost function. b) Calculate the firm's short-run marginal cost function. c) Graph the firm's short-run marginal and average (total, fixed, and variable) cost curves. d) Where does the short-run marginal cost intersect the short-run total average cost? Explain why this is so.A firm has the following production function: q = KL, where q is output, K is capital and L is labor. The price of a unit of capital is $1,000 and the price of a unit of labor is $500. The total cost includes the cost of capital and labor, as well as an additional $200 per unit of output for raw materials. The firm currently runs a single factory with 5 units of capital. Assume that capital is fixed in the short run. (a) How much does it cost to produce q units of output (in the short-run)? [The answer I expect is a particular function of q.] (b) Will the firm produce or shut down in the short run if the price of a unit of output is $300? Explain in at most one sentence.25. Molly operates a factory with a production function given by Q(K, L) = L+ 4K, where K is capital and L is labor. The factory employs 25 units of K and 12 units of L. If the production plant is relocated to take advantage of cheap labor so that the employment of K is reduced to 0, how many units of labor L would she need in order to maintain the same level of output as before? A) 48 B) 37 C) 32 D) 112
- Question 8 of 13 The following diagram depicts the production function of the farmers, where diminishing average product of labour is assumed. At A the average product of labour is 500,000/800 = 625 kg of grain per farmer. At B the average product of labour is 732,000/1,600 = 458 kg of grain per farmer. If you know that for 2,800 farmers the grain output is 894,000kg, then which of the following is/are correct? Kilogrammes of grain produced (thousands) 900 800- 700- 600- 500 400- 300- 200- 100- 0 0 400 800 B 1,200 1,600 Number of farmers 2,000 2,400 2,800 OA. The average product of labour when the labour input is 2,800 is 300. OB. The decreasing slopes of the rays from the origin to the production function along the curve indicate the decreasing average product of labour. OC. If the production function curve is an upward-sloping straight line, then there is no diminishing average product of labour. OD. It is possible that initially there is an economy of scale: for example, going from…Problem 7. A factory that you are managing has an hourly production process that can be represented by the following Cobb Douglas Production function: Q 20KL The price of one unit of capital per hour is $20 and the price of one unit of labour per hour is $20. You have been instructed to have a total cost of $1,000 or TC $1,000. Find the optimal amount of labour and capital that you will be using, and compute the amount of output..Consider a firm that has production function f(L,K)= 3L2/3K1/3. What is the expression for this firm’s Marginal Product of capital? MPK(L,K)= 3L2/3/K1/3. MPK(L,K)= 3L2/3/K2/3. MPK(L,K)= L1/3/K1/3. MPK(L,K)= L2/3/K2/3. MPK(L,K)= 2L2/3/K1/3.
