Consider the Cobb-Douglas Production function: = P(L, K) 17L0.1K 0.9 Find the marginal productivity of labor and marginal productivity of capital functions. Enter your answers using CAPITAL L and K, or your answer will not be recognized. Also, do NOT use negative powers...convert all powers so they are positive. Use the preview button to make sure your answer is entered correctly before you submit any answer(s)! PL PK=
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- 'roduction function: P(L, K) 13L0.3K0.7 Find the marginal productivity of labor and marginal productivity of capital functions. Enter your answers using CAPITAL L and K, or your answer will not be recognized. Use the preview button to make sure your answer is entered correctly before you submit any answer(s)! PL PKProblem 5 The production function of COVID vaccines for firm O is given by v° = VKL. and requires at least one unit of labor L and one unit of capital K, i.e. L>1 und K > 1. a) After a year and some thorough research, the production function changes to VO = V4KL. (I) Compute the marginal products with respect to labor L and capital K for both production functions ! (II) Which company's the marginal products is/are larger ? What happened to the original level of production after a year ? (III) Do the production functions exhibit increasing, constant or decreasing returns to scale ? b) Suppose now, we compare production functions of company O that discovered the vaccine to a second company M. The production function of M is given by VM = K0.6 L0.4 (I) Compute the marginal products with respect to labor L and capital K for this pro- duction function ! (II) If both companies used the same equal amount of labor L and capital K, which of them will generate more output ? (III) If the…4:34 D *3 all 100% I 2. 3 When the inputs price ratio (slope of cost line) is greater than the MRTS, (MPK/PK > MPL/PL) the producer should use .. to minimize the cost. A More labar C Mare labor and more capital B More Capital D| None of the above 4 The optimal production method A maximizes output regardiess of cost C minimizes the normal rate of return B| maximizes inputs. Dminimizes cost 5. Refer to the information provided in the following figure, If this firm's cost of labor is $10 per unit, and the isocost line represents a total cost 2000. How much is the cost of capital per unit? 100 q-300 -200 -100 200 Units of labor Linits of capital
- Derive formulae for the marginal products of the three inputs in the produc- tion function Q = 40K03L0.3R04. %DThe production function for good X in the table below exhibits increasing marginal returns to capital over what outout range? Production Function for Good X Choose Multiple Choice: Between o and 1,524 Between 2391 and 3,048 Between o and 2,991 • Between 3,016 and 2,945 L* MPx= (AQ/AK) AP=(Q/K) Marginal Product of Average Product of Labor Capital Output Capital Capital 10 57 5.7 5.70 20 324 26.7 16.20 30 657 33.3 40 1,072 41.5 26.80 50 1,524 45.2 30.48 60 1,976 45.2 32.93 70 2,391 41.5 34.16 2,724 33.3 34.85 9e 2,991 A 33.23 10e 3,048 5.7 30.48 11e 3,016 -3.2 27.42 120 2,945 -7.1 24.54A company manufactures two products, X and Y, and the joint-cost function of these products is given by c=x+4y where c is the total cost of producing v units of X and y units of Y Determine the marginal cost with respect to y when x=36 and y=16 b. The production function for a company's product is O-20, where is the output that results from /units of labor and & units of capital. The unit cost of labor and capital are $225 and $150, respectively. The company wants the total cost of puts to be $270,000 Find the number of units of capital and labor that maximize production
- What is the difference between economies of scale andeconomies of scope? How do firms consider these wheninvesting in processes?Q(K, L) = 4K²L2 Type your answers in all of the blanks and submit The production function of good x is as follow: a. What is the marginal production of capital with 16 labor and 4 capital? Type your answer her b. Calculate the slope of the isoquant when the entrepreneur is producing efficiently with 10 labors and 400 units of capital. Slope = Type your answer her (absolute value.) c. If we increase the amount of labor we use in our production process from 10 to 1000 units, how much change in capital is needed for us to stay on the same isoquant? Change in K= Type your answer here (Actual value, negative if decrease and positive if increase) d. Is diminishing return a characteristic of this production function? For labor? (yes/no) Type your answer her ;For Capital (yes/no)? Type your answer hereProvethatthetechnologyf(L,K)=L2+K2 exhibitsincreasingreturnstoscale. What is the formula for the average product of capital? For the total cost curve TC(q) = q3, prove the technology exhibits decreasing returns to scale
- (04.Suppose we are given (he constant returns to scale (CES) production function q= { ßa + aa }1/a a. Show that the marginal product of Beta is (g/B) and marginal product of Alpha (q/a)** b. Show that RTS = (2/B); I lence or otherwise shov that the ò =-1/(1-a) 1-aPlease no written by hand The estimated production function is Q = 12K ½ L1/4 The firm pays workers (L) and rents boats (K) in order to produce fish. Currently, the company has no fixed inputs and pays $12 per hour for labour (w) and $16 per hour for capital (r). The quantity of fish produced per day (Q) is 153. A. Derive the conditional input demand functions for labour (L) and capital (K) for IFC. B. What is cost-minimizing amount of labour and capital that IFC should hire and rent? C. Determine the minimum cost of producing 153 units of output? D. Use the isocost and isoquant to illustrate the optimal choice of this firm.Consider the input output table below Table (Inter) final Total (Agric) (Manuf) (Mining)demand (Inter) Agric 106 47 180 898 1231 Manuf 75 32 80 1167 1354 Mining 31 115 100 977 1223 PrimaryLabour 949 760 363 Capital 70 400 500 where: (Agric = Agriculture),( Manuf = Manufacturing),(Inter = !3! %3D Intermediate) A. Calculate the input coefficients and fill in the appropriate spaces in the table below. Use four (4) decimal places. Agric (Manuf) (Mining) Agric Manuf Mining Labour Capital