Suppose that a firm has production function ƒ(K, L) = K2a + Lª where a > 1. Assume that pk = PL where pk is the price of capital per unit and pL is the price of labour per unit. If the firm is producing at an optimal point then which of the following can we conclude? O The firm will use equal quantities of capital and labour. The firm will use twice as much capital as labour. The marginal rate of technical substitution will equal the price ratio. The firm will only use capital in production. More than one of the above.

When production is characterized by diminishing marginal productivity: increasing the amount of one input used means you must use more of another input. None of the answers is correct. unskilled workers are less productive than skilled workers. All Answers are correct. O output must increase with each additional unit of the input used in production.

Suppose you find that at a given input bundle the TRS=-2. Then you can conclude that at that input bundle: labour is more productive than capital O capital is more productive than labour labour and capital are equally productive O there is not enough information to answer

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A firm is currently producing 500 units of output daily by employing 60 units of labor daily at a price of $10 per unit and 30 units of capital daily at a price of $20 per unit. The marginal product of the last unit of labor employed is 3, and the last unit of capital employed is 5.  a. Given the above information, what does the firm's marginal rate of technical substitution, MRTSL,K, equal?  b. Indicate on the following diagram some point labeled A that is consistent with the information given in the question.

Suppose a firm's production function is Q=200L +5L2-0.08L³. Which of the following is the Average Production of Labor (APL)? Oa. 200+10L-0.24L² Ob. 10L-0.24L² Oc. 5L-0.08L² Od. 200+5L-0.08L²

Suppose that this conveyor-manufacturing firm has another location and would like you to evaluate the input mix decisions at this new location. Here is all you know about the newlocation. The marginal rate of technical substitution is currently 0.5. The marginal product of labor at its target level of output is 60 rollers per hour. What is the marginal product of capital? Ifthe rental rate for capital is $24 per hours at this location and the wage paid to labor is $12 per hour, could this location be minimizing the costs of producing its target level of output? Explain briefly.

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 gpt

A company has the following production function for its product, f(k, I) = k"/2/1/2. It faces input prices v = 5 for capital and w = 20 for labor. How much does the firm use of each input if it wants to produce 10 units of its product? O a. I= 4, k = 25 O b. / = 5, k = 20 O c. 1= 20, k = 5 O d. 1= 25, k = 4 Clear my choice Suppose the market demand for a good is Qº = 2000 – 8p and market supply is QS = 5p + 700. There are 10 %3D firms with exactly the same cost function. How much does each firm produce? O a. 100 O b. 120 O c. 140 O d. 200 Clear my choice

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).