If a price-taking firm's production function depends only on labor L and is given by q = 2L2, then the unconditional demand for L is given by O a. L= qlw O b. L = q? O c. L=( O d. L= ( Clear my choice
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- Suppose a firm has a production function q = f(L,K) = 3L + 2K, and the factor prices are w = $3 and r = $3. If the firm wants to produce 60 units at the minimum cost possible, how much would it cost to produce those 60 units? (hint: remember perfect substitute technology yields corner solutions for L and K). O $60 O $90 $120 $30 O $150When a firm produces one unit, the variable cost is $7. When the firm produces two units, the variable cost is $10. When the firm produces three units, the variable cost is $12. What is the marginal cost associated with three units of production? Select one: O a. 3 O b. 7 O c. 2 O d. 03. Answer all parts (a)-(e) of this question. Consider the following production function: Q = 3K&L, with marginal products given by L3 MPL = K and MPK Define the unit prices of L and K as w and r, respectively. Finally, assume that the firm takes the price of its product, p, as given and maximizes profits. L3 K3 (a) Imagine capital is fixed at Ko = 1 in the short run. What is the short-run cost function of the firm? Explain briefly. (b) (c) (d) (e) when rw = 1? What is the long-run cost function of the firm? What is the long-run supply function of the firm? What is the profit function of the firm? Now suppose that set-up costs are £1. What is the shut down rule of the firm
- Suppose that Marie produces milk q using her own labor l and cattle k using the production functionq = f(k, l) = k2/3ℓ1/3Although Marie does not need to pay anyone to use either input, the opportunity costs of labor and cattle are w = 1 and v = 16, respectively, and P is the price of milk. a) Suppose that Marie’s stock of cattle is fixed at k0 = 8. Set up her short run cost minimization problem and find her labor demand ℓ(q) and cost function SC(q). b) Find Marie’s short run marginal cost SMC(q) and average cost SAC(q) functions and find the quantity at which short run average cost is minimized. c) Set up Marie’s short run profit maximization problem and find her short run supply curve q(P).A firm's production function is Q = 100L.0 K-4. The firm's input prices are PL = $40 and PK = $30. The firm wishes to produce Q = 3,000 units of output and minimize the cost of production. How much labor (L) should the firm employ? O A. L=20.96. O B. L=31.45. O C. L=34.26. O D. L=38.45. O E. L=41.22. QUESTION 2 A firm estimates its production function as Q = -2.4 + 20*L -.5*L2 + 30*K -1.00*K2 + 15*F -.3*F2. Total cost is TC = $2*L + $2.5*K + $1.75*F. The firm wishes to produce 400 units of output. Use Excel to find the cost minimizing amounts of L, K and F. How much F (Fuel) should the firm use? O A. F=7.90. O B. F=9.58. O C. F=10.75. O D. F=12.63. O E. F=14.88.A firm has two opportunities for a new plant location, one is in China and the other is inMexico. The firm's production function is given by q = L 0.5 K 0.5 , In China, the cost of laboris w=$15 and the cost of capital is r=$5. In Mexico, w=$10 and r=$10. The firm wants toproduce 100 units of output. Which location should the firm choose for their new plant?Explain why.Note: Please round the optimal amounts of capital and labor at each location to the nearest whole number when making your calculations.Hint: cost-minimization rule.
- Suppose the long-run production function for a competitive firm is f(x1,x2)= min {x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2. .a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. .b. Draw the conditional input demand functions for labor and capital in the x1-y and x2- y spaces. .c. Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? .d. Write down the formula and draw the graph of the average cost function, as a function of y. .e. Write down the formula and draw the graph of the marginal cost function, as a function of y.When making a choice between factor inputs such as labor or equipment, or between two different kinds of equipment, a profit maximizing firm will choose O the cheaper, lowest price item, regardless of its productivity O the highest productivity item, regardless of its price O the item which yields the most productivity per dollar of price O none of the aboveA perfectly competitive firm's production function is Q=4LK where Q is the amount produced, L is the amount of labour hired and K is the amount of capital used. P is the price that the firm gets for its product. What is the marginal revenue product of labour? O 8PK O 4L O 4PK O PL
- if marginal product is given by 500 - 5Q4 find the value of Q where marginal product is at its maximum. Select one: O 1000. O 1/5 O 500. O5. O 100.Consider the following production function: q = 9LK + 6L² – Assuming capital is measured on the vertical axis and labor is measured on the horizontal axis, determine the value of the marginal rate of technical substitution when K= 30 and L= 10. MRTS = -. (Enter a numeric response using a real number rounded to two decimal places.) 20 tv MacBook Air F6 FB 10 F3 23 2$ & з 4 6 7 8 { [ E Y U P D F G J K > C V N M command option - .. .- BFirms typically experience decreasing marginal returns to labor at Select one: O A. low; congestion OB. low; specialization OC. high; specialization O D. high; congestion levels of employment due to