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- What is the difference between economies of scale, constant returns to scale, and diseconomies of scale?If two painters can paint 200 square feet of wall in an hour, and three painters can paint 275 square feet, what is the marginal product of the third painter?Suppose there are two inputs for production, labor and capital. The firm’s production process isdefined by the following production functiony=f(L,K).Howdoweinterpretthefirm’smarginalrateof technical substitution? a)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same cost level b)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm produces one more unit of output c)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same level of production d)a) and b) are correct e)a) and c) are correct
- Production Function. Consider the Cobb-Douglas production function discussed in class:F(K, L) = AK^1/3 L^2/3. Suppose that parameters are initially A = 1, K = 150, and L = 10. d) Suppose that the quantity of labor L doubles. Calculate Y, w, r, Y/L, and K/L. Com-ment on how and why these numbers changed relative to (c) and why they did so. E) Suppose that the quantity of capital K doubles as well. (So now both K and L aretwice their previous value). Calculate Y, w, r, Y/L, and K/L. Comment on how thesenumbers changed relative to both their initial values, and their values in (d).3. Theo employs labor at a competitive wage (W) of $3 per unit, and he employs capitalat a competitive rental rate (R) of $6 per unit.a. State the cost-minimizing rule. You must provide both a written statement of it, and state it as anequation.b. At Theo’s current combination of labor and capital, the marginal product of labor (MPL) is twiceas large as the marginal product of capital (MPK). Is Theo currently employing the optimal ratio oflabor and capital? If not, how should he adjust his hiring of labor and/or capital? Explain.uppose a Cobb-Douglas Production function is given by the following:P(L,K)=60L^0.8K^0.2where LL is units of labor, KK is units of capital, and P(L,K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $900 and each unit of capital costs $3,600. Further suppose a total of $900,000 is available to be invested in labor and capital (combined).A) How many units of labor and capital should be "purchased" to maximize production subject to your budgetary constraint?Units of labor, LL = Units of capital, KK = B) What is the maximum number of units of production under the given budgetary conditions? (Round your answer to the nearest whole unit.)Max production = units
- 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 gptAnswer the Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output ifit the firm decides to triple both the amount of labor and capital?2. State the optimization problem of the firm.3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product ofCapital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combinationof K and L that the firm should use to produce the maximum possible output. Do not solvethe problem using the Lagrangian method.Note: The tangency conditions just states that the slope of the production function must beequal to the slope of the isocost function.5. What is the maximum possible output that the firm could earn given the constraint it faces?Production Function. Consider the Cobb-Douglas production function discussed in class:F(K, L) = AK1/3 L2/3. Suppose that parameters are initially A = 1, K = 150, and L = 10. D) Suppose that the quantity of labor L doubles. Calculate Y, w, r, Y/L, and K/L. Com-ment on how and why these numbers changed relative to (c) and why they did so.
- please asnwer the question in the image Some economists believe that the U.S. economy as awhole can be modeled with the following productionfunction, called the Cobb–Douglas production function:Y 5 AK1/3L2/3,where Y is the amount of output, K is the amount ofcapital, L is the amount of labor, and A is a parameterthat measures the state of technology. For this productionfunction, the marginal product of labor isMPL 5 (2/3) A(K/L)1/3.Suppose that the price of output P is 2, A is 3, K is1,000,000, and L is 1,000. The labor market is competitive,so labor is paid the value of its marginal product.a. Calculate the amount of output produced Y and thedollar value of output PY.b. Calculate the wage W and the real wage W/P. (Note:The wage is labor compensation measured in dollars,whereas the real wage is labor compensationmeasured in units of output.)c. Calculate the labor share (the fraction of the value ofoutput that is paid to labor), which is (WL)/(PY).d. Calculate what happens to output Y,…The table shows total production of a firm. If units of labour (L) increase, find below. 2 marks Units of Labour Total Product (TP) Marginal Product (MP) Average Product (AP) 0 0 1 80 2 200 3 330 4 400 5 450 6 480 7 490 8 480 Compute the marginal product of labour (MP) from first to eighth units of labour. Now compute the average product (AP) of the various quantities of labour and enter them into table. There are increasing return to labour from the first through the ---------------- units of labor and decreasing return from the --------------through eighth units. d. When total production is increasing, marginal product is (positive, negative) --------------- and when total production is decreasing, marginal product is ----------------The table shows the total production of a firm. If units of labour (L) increase, find below. Units of Labour Total Product (TP) Marginal Product (MP) Average Product (AP) 0 0 1 80 2 200 3 330 4 400 5 450 6 480 7 490 8 480 Compute the marginal product of labour (MP) from first to eighth units of labour. Now compute the average product (AP) of the various quantities of labour and enter them into the table. There are increasing return to labour from the first through the ---------------- units of labour and decreasing return from the --------------through eighth units. When total production is increasing, marginal product is (positive, negative) --------------- and when total production is decreasing, marginal product is ----------------