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- Suppose a firm uses capital K and labor L to produce output Q with the following production function: 1 Q=4KL + = 1² 3 (a) Find the marginal product of capital and the marginal product of labor. (b) Find the average production of capital and the average production of labor. (c) Does this production function have increasing, constant, or decreasing returns to scale? Explain. (d) Find the marginal rate of technical substitution (RTS). (e) Use your result in (d) to find the elasticity of substitution. (f) Find the contingent demand functions for capital and labor if w is the price of labor input and v is the price of capital input.The marginal cost of producing the xth box of light bulbs is 4 + x2 dollars per box. Determine how much is added to the total cost by a change in production from x = 20 to x = 80 boxes. 1,000Labor When the firm uses 40 units of labor, how much output does it produce? 1,600 units B 2,800 units C none of the above D 4,000 units E 400 units
- Refer to the graph below: y2 The graph above illustrates a production set of a firm. (a) Which assumption(s) do(es) the production set violates? Explain. (b) Suppose the firm decided to scale all inputs up or down by some amount t > 0. What will happen to the level of output?A farmer can produce f(x,y) = 208-√4x² + y² units of produce by utilizing x units of labor and y units of capital. (a) (b) (c) Calculate the marginal productivities of labor and capital when x = 12 and y = 10. Let h be a small number. Use the result of part (a) to determine the approximate effect on production of changing labor from 12 to 12+h units while keeping capital fixed at 10 units. Use part (b) to estimate the change in production when labor decreases from 12 to 11.5 units and capital stays fixed at 10 units. (a) The marginal productivity of labor when x = 12 and y = 10 is (Simplify your answer.)oboard S Font Paragraph S Sensitivity Styles Editing Voice A Cobb-Douglas production function for new company is given by FF(KK, LL) = KK3/5LL2/5 where K represents the units of capital and L represents the units of labor. Suppose units of labor and capital cost $200 and $100 each respectively. If the budget constraint is $30,000, find the maximum production level for this company. VAAAWMMAA AAAAAAAAA SAAAAAAA
- Fill in the missing parts in the following tables to illustrate the behavior of production and costs in the short-run; then determine the optimal level of production according to the number of inputs you are intending to use. Output Units Land Square Meters Capital Egyptian Pounds Labor Units 0 20 40000 0 1000 20 40000 5 1600 20 40000 8 2100 20 40000 11 2500 20 40000 14 2600 20 40000 17 Output FC VC TC MCL MPL AVC AFC ATC 0 1000 1600 2100 2500 2600 -Hint Consider land and capital as fixed factors, while labor units as variable factors. The cost of land is L.E20 per square meter. The interest rate on capital is 10%. The average wages per unit of labor is L.E1500.A firm uses 3 factors of production. Its production function is f(x, y, z) = min{x3/y, y2, (z4 − x4)/y2}. If the amount of each input is multiplied by 6, its output will be multiplied by A.) 216 B.) 36 C.) 6 D.) 0.16 -the Answer is 36, Please explain in detail why this isdien There are two factors in a production function y = x 113 x₂¹1³. The market price of each unit ofy is p=3, and the factor prices are w₁=1 and W₂=2 for x₁ and X₂ respectively. variable (a). Calculate your cost function as a function of y if X, and x₂ are both barible factors. (b). Now derive the functions of average and marginal cost and plot them against quantity (C). Solve for your optional output of y. Calculate the ratio of two factors (X₁/X₂) (d). In the short run the fixed factor is set at X₂=1. What is the new optimal output level now?
- Problem 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…Picture Tools 16285711986112063eel9ba0 69816244 (Read Only Sman References Mailings Review View Format Picture Shape Y Bring to Fre Picture Border Send to Bac Position Picture Effects Text Wrappr Picture Styles Arrange 2. 6 Question 2. 1. Widget factory Inc. in Wisconsin has the following production function: F(L,K) = 2L/2 K/2 L represent the number of labour hours. Workers at this factory are paid an hourly wage of $30 and they rent capital at $25/hour. Since this is a competitive market, the factory output the factory gets per is output is $50 per unit. Let's pretend the firm operates in the short run with capital fixed at 900, how many factory workers would Widget Factory Inc employ? What is their profit rate? Question 3.What is the per unit opportunity cost of product X as production moves from point A to point F? A) 2/5 B) -2/5 C) 5/2 D) -7/6
