A country's Cobb-Douglas production function is as follows: Y= 5K^(1/2)L^(1/2). If this country has 30,000 unit of capital and 700 workers, find the real wage approximately. Select one: a. 1.21 b. 0.85 c. 0.99 d. 0.55 e. 0.66
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- A country's Cobb-Douglas production function is as follows: Y= 5K^(1/2)L^(1/2). If this country has 20,000 unit of capital and 500 workers, find the real wage approximately. Select one: a. 0.85 b. 0.99 C. 0.55 d. 0.66 e. 1.21The Whoville Marble Collective (WMC) makes fancy marbles for picky Whos. WMC's output is given by Q = 20K0.75L0.25, where Q is WMC's annual output (measured in 1000s of marbles), K is their annual capital input and L is their annual labor input. WMC's capital input costs PK = $8000 per unit and their labor input costs PL = $25000 per unit. Assuming that WMC's annual production budget is B = $800,000, their maximum annual output is ... = = 412,891 marbles. 726,085 marbles. 578,634 marbles. = 857,232 marbles.1. The Primary Metals production function in Table 7.4 of the MMH textbook, holding nonproduction workers constant, can be roughly expressed as Q = 100*L.08*K.37. Use this function to answer the following. Suppose a firm wishes to produce 1200 units of Q. Use an Excel Spreadsheet to find the MRTSLK in adding a 10th unit of Labor. Conduct your analysis using an Excel Spreadsheet and changing Labor by 1, 2, 3, etc., that is, use integer values of L only. In absolute value terms, the MRTSLK when we add the 10th unit of L is ______. A. 114.9. B. 18.4. C. 11.6. D. 7.5. E. 3.6. 2. This is a continuation of the previous problem. Suppose a Primary Metals company’s ratio of PL to PK is 1.40. What is the optimal (cost minimizing) combination of L and K that should be employed by the firm to produce Q = 1200? Conduct your analysis using an Excel Spreadsheet and changing Labor by 1, 2, 3, etc., that is, use integer values of L only. Use a Spreadsheet and not Excel Solver. The optimal L = _____…
- A firm’s only variable factor is labour and it produces a single product, X. It also has fixed costs. The short-run production function is; X=-0.1L3 + 6L2 + 12L. Where X is the output in tons, and L is the number of persons employed. How many persons are employed if the average physical product of labour is maximized? How many persons are employed if the marginal physical product of labour is maximized? What is the quantity of X when average variable cost is minimized? If the weekly wage is $360 and the price of X is $30 per ton, how much X should be produced to maximize profits?A firm’s only variable factor is labour and it produces a single product, X. It also has fixed costs. The short-run production function is; X=-0.1L3 + 6L2 + 12L. Where X is the output in tons, and L is the number of persons employed. How many persons are employed if the average physical product of labor is maximized? How many persons are employed if the marginal physical product of labor is maximized? What is the quantity of X when the average variable cost is minimized?The firm employs workers for R100 per day. Each unit sells for R30. The firm’s production function is as follows: Labour Output 1 6 2 11 3 15 4 18 5 20 6 21 Q3.2.1 Re-draw the table above and add two columns one showing the Marginal Physical Product and the other column showing the value of the marginal product of labour MRP) at each input level.
- Sam Malone is considering renovating the bar stools at Cheers.The production function for new bar stools is given byq = 0.1k 0.2l0.8 where q is the number of bar stools produced during the renovation week, k represents the number of hours of bar stoollathes used during the week, and l represents the number ofworker hours employed during the period. Sam would like toprovide 10 new bar stools, and he has allocated a budget of$10,000 for the project.a. Sam reasons that because bar stool lathes and skilled barstool workers both cost the same amount ($50 per hour),he might as well hire these two inputs in equal amounts.If Sam proceeds in this way, how much of each input willhe hire and how much will the renovation project cost?b. Norm (who knows something about bar stools) arguesthat once again Sam has forgotten his microeconomics.He asserts that Sam should choose quantities of inputs sothat their marginal (not average) productivities are equal.If Sam opts for this plan instead, how much of…(b) Prove that the per-worker production function has the following properties: f'(k) ≥ 0, lim f'(k)= +∞, and k-0 lim f'(k) (c) Assume that the production factors receive their respective marginal products. Derive the expressions for the wage rate, W, and the rental rate on capital, r + 8, when technology is Cobb-Douglas. What happens to (W,r) as k 0 and as k→ ∞o? Derive the expression for the factor price frontier (FPF), i.e. the expression linking W and r, and illustrate it graphically. Show what happens to the FPF if general productivity increases. = 0..Suppose the hourly wage is $10 and the price of each unit of capital is $25. The price of output is constant at $50 per unit. The production function isf(E, K) = E 1/2K 1/2so that the marginal product of labor isMPE = (1/2)(K/E) 1/2If the current capital stock is fixed at 1,600 units, how much labor should the firm employ in the short run? How much profit will the firm earn?
- Q2. The table 1 below is shown the production theory of labour for company D'LIMAU Sdn Bhd. Input X Input Y Total Product Average Product (AP) Marginal Product (MP) (TP/Q) 0 20 80 180 230 1 1 1 1 1 1 1 1 0 1 2 3 4 5 6 7 270 270 2102wrQ Suppose the long-run cost function is given by: C(w, r, Q) = (W+1)" What would be the conditional demand for labor and capital respectively? 2rQ 2wQ (w+r)² (w+r)² Q (w+r)² (w+r) 212Q 2w²Q (w+r)? (w+r)2 212Q 2w²Q (w+r) (w+r)3The table shows the daily production of Papaya Co., that supplies papayas to hotels and restaurants in Manila Price of 1 kg. =P50, Daily wage per What is the marginal product worker P500 of each of the 6th to 10th workers? MP No. of Total AP (kg) [Select] (kg) Law of Diminishing marginal returns sets in after how many workers? Workers Product (kg) per per worker worker [Select] 0 5 10 15 20 25 30 35 0 1500 4500 10500 18000 24000 27000 28000