The wage rate is $25 per hour and the cost of capital is $50 per hour. At the current output, the firm's MPL is 5 units and MPK is 15 units. In order to maximize profit without changing the production level, the firm should Select one: O A. hire more labour and rent less capital O B. keep its current level of labour and capital inputs. OC. rent more capital and hire less labour O D. hire less labour and rent less capital
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- A firm uses two inputs in production: capital and labor. In the short run, the firm cannot adjust the amount of capital it is using, but it can adjust the size of its workforce. What happens to the firm’s average total cost curve, the average variable cost curve, and the marginal cost curve when a. the cost of renting capital increases?b. the cost of hiring labor increases?which of the following statements is true?A) The MP of labor is always negative at short runB) The MP of labor is increasing at short run because the stock of capital fixedC) Adding more labor will produce progressively greater increments of outputD) The MP of labor after an increase the beginning declining while remaining positive at short run7 The Paunch Burger restaurant chain currently produces 250,000 units of output by using 2,400 units of capital and 520 units of labor. Paunch Burger’s marginal rate of technical substitution (MRTS) of labor for capital is 3.5. If Paunch Burger’s regional manager wants to produce the same amount of output but increase the company’s use of capital by 175 units, how many units of capital will Paunch Burger now need to use?
- A firm produces good Y with just 2 factors: Capital which is fixed in supply and labour which is variable. Identify the stages of production in the diagram and explain why the firm still hire labour even though it is in the range of diminishing returns. What is the number of workers after which diminishing marginal returns starts? Is this a short run or long run phenomenon? Labour (units) 1 2 3 4 5 6 7 8 9 Total Product (TP) in Units 8 15 24 30 35 37 38 38 36 Average Product (AP) in units 8 7.5 8 7.5 7 6.17 5.43 4.75 4 Marginal Product (MP) in units 8 7 9 6 5 2 1 0 -2A producer has the following technology.y= 6K^(1/2)L^(1/2) a) Prove formally that the production function exhibits constant returns to scale (use “λ” argument). b) Find analytically MPL and MPK. Is MPL increasing, decreasing, or constant inL? Is MPK increasing, decreasing, or constant in K? c) Short-run: Given stock of capital ̄K= 1 find labor demand (formula) of a competitive firm. Find equilibrium real wage rate if labor supply is given by Ls= 9 (one number). d) Assume again ̄K= 1 and that Ls= 9. The government adopts a real minimum wage of wmin/p=(3/2). Find labor demand (one number) and the unemployment rate (one number). Please depict the equilibrium on a graph with the real wage on the vertical axis and labor on the horizontal axis, indicating the equilibrium quantity of labor, wage, and unemployment, as well as the relevant curves. e) Find the cost function given prices of inputs wK= 4 and wL= 1 (formula). Plot the cost function on a graph, indicating the slope of the cost…Can you put a solution to this? Instruction: (see other instructions below, for the submission of answer sheet) A. Complete the Column for MRS. Show your solution for each answer, Number each solution that corresponds to each unknown MRS. B. Graph the Labor-Capital function, making sure that Labor units are in the horizontal axis MRS = change in K/ change in L change in K = final K - initial K change in L = final L - initial L MRS = 26-30 /2-1 MRS = -4/1 MRS = - 4 Units of Labor Capital MRS 1 30 0 2 26 -4 3 22.5 (1) 4 19.5 (2) 5 17 (3) 6 15 (4) 7 13.5 (5) 8 12.5 (6) 9 12 (7) 10 12 (8)
- onsider a producer with budget C = 200 who can buy labor L at a wage w = 10 and capital K at a price r = 5. The producer has the following production function F(K,L) = 3K1/3 L2/3 . a. Does F(K,L) exhibit increasing, decreasing, or constant returns to scale? Show your work. Consider a new production function F(K,L) = K1/3 L2/3 , where is a? ? positive constant not equal to 3. Does the new production function exhibit increasing, decreasing, or constant returns to scale? b. Using F(K,L) = 3K1/3 L2/3, find the optimal bundle. Show your optimal bundle on a plot (this should include isoquant and isocost curves). c. Suppose the budget is reduced to C = 100 and then C = 50. Find the new optimal bundles. Plot these bundles, along with the initial optimal bundle, on one plot. Draw the expansion path PLEASE SHOW GRAPHS do not use chat gptKA. A firm produces output with the production function, Q = F(K, L) = K0.5 L0.5 with r=4 and w= 2. The firm is using K=16 and just enough L to produce 16 units of output in the short run. How much could the firm save if it were producing 16 units in the long run?1) a. What is a production function? How does a long-run production function differ from a short-run production function?b. Explain the term “marginal rate of technical substitution.” What does a MRTS = 4 mean?
- During the 1920s, Charles Cobb and Paul Dougkas modeled totalproduction output P (of a firm, company or entire economy) as a function of labourhours involved x and capital invested y (each includes the monetary worth of allbuildings and equipment). The Cobb-Douglas production function isP(x, y) = k x^α y^(1−α),where k ad α are constants representative of a particular firm or economy.(1) Show that doubling of both labor and capital results in doubling productionP.(2) Suppose a particular firm has the production function for k = 120 andα =3/4. Assume each unit of labor costs $250 and each unit of capital costs$400, and that the total expense for all costs cannot exceed $100,000. Findthe maximum production level for the firm.(3) Compute the production level at x = 64 and y = 81. If the capital isdecreased by 3 units, by how many units the labor should be adjusted toso that there is not change in production level.Suppose the production data of XYZ company mentions labor (L) as a variable input and machine (K) as a fixed input. Complete the table as XYZ increases its number of laborers (L). L TP MP AP 1 100 100 100 2 220 120 110 3 270 1) _____ 90 4 270 2)_____ 3)_____ 6 4)_______ 5)_____ 50 8 180 6) ____ 7) ____Hi- please answer both A and B A construction company has two types of employees: skilled and unskilled. A skilled employee can build 1 yard of a brick wall in one hour. An unskilled employee needs twice as much time to build the same wall. The hourly wage of a skilled employee is $15. The hourly wage of an unskilled employee is $8. a) Write down a production function with labor. The inputs are the number of hours of skilled workers, LS, the number of hours worked by unskilled employees, LU, and the output is the number of yards of brick wall, Q. b) What is the cost-minimizing way to build 100 yards of a wall?