10. A firm produces output according to the production function Q = F(K, L) = 4K +8L. a. How much output is produced when K= 2 and L= (LOI, LO2) b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 32 v c. How does your answer to part b change if the wage but the rental rate on capital remains at $20 per hour? 3? Units of output? rate decreases to $20 per hour
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- Suppose that the production function for Hannah and Sam's home remodeling business is Q=f(L,K) Q=1040.2K0.3 Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $2,000 per week. a. What is the least-cost input combination for remodeling 100 square feet each week? Instructions: Round your answers to 2 decimal places. units of labor and units of capital. b. What is the total cost? Instructions: Round your answer to 2 decimal places.Suppose that the production function for Hannah and Sam's home remodeling business is Q = F(L,K) Q = 10L0.1K0.4.Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $1,000 per week.a. What is the least-cost input combination for remodeling 400 square feet each week? Instructions: Round your answers to 2 decimal places. units of labor and units of capital. b. What is the total cost? Instructions: Round your answer to 2 decimal places. $ .revised jrl 08-11-2011A firm produces output according to a production function: Q = F(K,L) = min {4K,8L}. a. How much output is produced when K = 2 and L = 3? 192 Numeric ResponseEdit Unavailable. 192 incorrect.unit(s) b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 8 units of output? Capital: 80 Numeric ResponseEdit Unavailable. 80 incorrect. Labor: 480 Numeric ResponseEdit Unavailable. 480 incorrect. c. How does your answer to part b change if the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour? multiple choice Capital and labor increase. It does not change. Capital increases and labor decreases. Incorrect Capital decreases and labor increases.
- Firm B uses capital, K, and labor, L, to produce a single output using a fixed-proportions technology that can be represented by the production function f(K, L) = min{K, 5L}. If one unit of capital costs r= $2 and one unit of labor costs w $5, and there are no fixed costs, how much it costs for Firm B to produce 500 units of output? $500 O $1,000 $1,500 $2,000AlphaBee's production function is given by frk.l) = [ min{31,2k) 10. AlphaBee can sell its product at $30 per unit, can hire as many workers as necessary at wage w = $15, and use as much capital as necessary at a price r= $19. It does not face fixed costs. How many units does the firm produce? Hint: First, find AlphaBee's cost function. Enter a numerical value below. You may round to the second decimal if necessary.Suppose that a firm's production function is given by F(K,L) = given by MPK= O 3 2 1 1 2 L² + K 2 2 and MPL = 1 1 1 1 [***** ( 2 L² +K ² 3 2 K 3 2 2 determined by (K,L) = (144,16) fall, and what is the slope of the isoquant line, or marginal rate of technical substitution, at that point? It falls on the isoquant line determined by a production level of q=4, and the slope of the isoquant line at this point is 3. It falls on the isoquant line determined by a production level of q = 4, and the slope of the isoquant line at this point is - 1/3. It falls on the isoquant line determined by a production level of q = 4, and the slope of the isoquant line at this point is - 3. It falls on the isoquant line determined by a production level of q = 64, and the slope of the isoquant line at this point is - 3. 1 L²+K 2 2 2 1 3 L 1 - 23 2 in which case the marginal product of capital and labor are " " respectively. On which isoquant line does the production level
- Q1.The following is a Cobb-Douglas production function: Q = 1.75K0.6L0.5. What is correct here? * -This production function displays constant returns to scale -This production function displays increasing returns to scale -A one-percent change in L will cause Q to change by one percent -This production function displays decreasing returns to scale Q2. For studying demand relationships for a proposed new product that no one has ever used before, what would be the best method to use? * -consumer surveys, where potential customers hear about the product and are asked their opinions -double log functional form regression model -ordinary least squares regression on historical data -market experiments, where the price is set differently in two marketsLet us consider the cost implications of the short-run production schedule from assignment number 7, where capital was fixed at 2 units of capital. Labor: 0 1 2 3 4 5 6 7 8 9 Output: 0 6 24 60 120 170 210 240 260 270 In this scenario, since we only have two inputs (Capital and Labor), and since the amount of capital is fixed, the cost of total cost capital would also be Total Fixed Cost (TFC) and since labor is variable, the total cost of labor would be Total Variable Cost (TVC). In that context, assume that the cost of capital is $40 per unit per period, while the cost of labor (or wage rate) is also $30 per unit of labor per period. (a) Use this information set up a diagram (using excel) that shows total cost (TC) and total variable cost (TVC) of the firm per period in the short run with the level of output on the horizontal axiLet us consider the cost implications of the short-run production schedule from assignment number 7, where capital was fixed at 2 units of capital. Labor: 0 1 2 3 4 5 6 7 8 9 Output: 0 6 24 60 120 170 210 240 260 270 In this scenario, since we only have two inputs (Capital and Labor), and since the amount of capital is fixed, the cost of total cost capital would also be Total Fixed Cost (TFC) and since labor is variable, the total cost of labor would be Total Variable Cost (TVC). In that context, assume that the cost of capital is $40 per unit per period, while the cost of labor (or wage rate) is also $30 per unit of labor per period. Also, use this information to then set up another diagram showing the firm's short run marginal cost (MC), average total cost (ATC), and average variable cost (AVC), with output on the horizontal axis (For the marginal cost, remember that when you graph marginal values you should always put them in…
- F (L, K) = L0.2K0.7, The wage rate (price per unit of labour) is w = 2 and the capital rental rate (price per unit of capital) is r = 7. Does this production function exhibit increasing, decreasing or constant returns to scale? Explain. What is the marginal productivity of labour and the marginal productivity of capital for (L,K) = (1,1)? Would a firm (which minimises costs) use this combination of labour and capital? Explain. If your answer is yes, then what would be the quantity of production for which the company would use this combination?A firm produces output according to a production function Q = F(K, L) = min {4K, 8L}. a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 8 units of output? c. How does your answer to part b change if the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour?Suppose that a firm's production function is given by Q = 2KL, where Q is quantity of output, K is capital, and L is units of labor. Note that MPL = K and MPK-L. The price per unit of labor and capital are $30 and $50 respectively. How many units of labor and capital should the firm use if it wants to minimize the cost of producing 480 units of output? L = 10, K = 24 L=12, K 20 L = 20, K = 12 L = 24. K = 10