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2. Consider again the production function for lava lamps: () = KL -L'. a. Sketch a graph of the isoquants for this pro...
1. Suppose that the production function for lava lamps is given by Q = KL -ľ, where is the number of lamps produced pe...
1. Suppose that the production function for lava lamps is given by Q = KL -ľ, where is the number of lamps produced per year, K is the machine-hours of capital, and L is the man-hours of labor. Suppose K = 600. a. Draw a graph of the production function over the range L = 0 to L = 500, putting L on the horizontal axis and on the vertical axis. Over what range of L does the production function...
b. Does this production function have an uneconomic region? If yes, find the region. c. Based...
b. Does this production function have an uneconomic region? If
yes, find the region.
c. Based on your answer to (b), sketch a graph of two isoquants
Q1 and Q2 withQ1 < Q2.
1. (12 points) Consider the production function Q = KL2-L", and answer the following questions. a. (4 pts) Does this production function exhibit diminishing marginal product of capital? Diminishing marginal product of labor? Explain.
Consider the Leontief production function F(KL) = min {K,L], where capital K and labor L have...
Consider the Leontief production function F(KL) = min {K,L], where capital K and labor L have respective positive input prices r and w. (a) Why is it that the cost-minimizing firm sets K 5. L? (b) What is the cost function? (c) How would your answer to part (b) change, if at all, if rw 0? Explain.
1. A production function is given by f(K, L) = L/2+ v K. Given this form,...
1. A production function is given by f(K, L) = L/2+ v K. Given this form, MPL = 1/2 and MPK-2 K (a) Are there constant returns to scale, decreasing returns to scale, or increasing returns to scale? (b) In the short run, capital is fixed at -4 while labor is variable. On the same graph, draw the 2. A production function is f(LK)-(L" + Ka)", where a > 0 and b > 0, For what values of a and...
The three isoquants in the graph below refer to production levels of 100 (red), 200 (green),...
The three isoquants in the graph below refer to production levels of 100 (red), 200 (green), and 255 (blue). As long as the quantity of capital (K) and labor (L) used in the production process lies on the line a, whenever L is tripled K is also tripled. - =100 =200 - =255 L OPTIONS BELOW a Does this production function exhibit increasing, decreasing, or Increasing constant returns to scale? Decreasing Constant Not enough Information OPTIONS BELOW b Iftold you...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital,...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w., and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p. 11. Consider the production function: f(KL)=K+L. Let w and r denote the price of labor and capital, and...
7. Suppose a firm's production function is Q-min(L,K). (This means the level of O produced is...
7. Suppose a firm's production function is Q-min(L,K). (This means the level of O produced is the smaller of L and K) a. Graph some isoquants for this firm. b. Let w = 2, r= 1, and suppose the firm's expenditures are C-12. What are the firm's demands for L and K? What is the share of labor in the cost of output? c. Now let w rise to 3. What are the firm's new demands for L and K?...
2. Consider a firm producing pizza with production function q = KL, that faces input prices...
2. Consider a firm producing pizza with production function q = KL, that faces input prices w= $10 and r = $100 for labor and capital, respectively. a. Derive the isoquant equation. Find the isoquant of an output q = 1. Draw it in a figure with l in the horizontal axis and k in the vertical axis. b. Does this firm's production exhibit increasing, decreasing or constant returns to scale? Briefly explain c. Find the labor demand, and the...
8. Suppose that the following graph shows a few of the isoquants for a firm's production...
8. Suppose that the following graph shows a few of the isoquants for a firm's production function for producing park benches. The firm's production function is Q = 20KVL. Suppose that the firm's goal is to produce Q= 160 in the cost minimizing way. The cost of a unit of capital (K) is $32 (r=$32) and the cost of a unit of labor is $32 (w=$32). a. Show the firm's cost minimizing isocost on the graph when the firm is...
4. Consider the production functions given below: a. Suppose that the production function faced by a...
4. Consider the production functions given below: a. Suppose that the production function faced by a milk producer is given by Q = 40.5 20.5 = 4VK VL, where MPx = 2K-0.5 20.5 = 2 and MP, = 2 K0.5L-05 = 2 * i. Do both labor and capital display diminishing marginal products in the short run? ii. Find the marginal rate of technical substitution for this production function. (Hint: The MRTS = 1) iii. Does this production function display...
1. Suppose that the production function for lava lamps is given by Q = KL -ľ, where is the number of lamps produced per year, K is the machine-hours of capital, and L is the man-hours of labor. Suppose K = 600. a. Draw a graph of the production function over the range L = 0 to L = 500, putting L on the horizontal axis and on the vertical axis. Over what range of L does the production function...
b. Does this production function have an uneconomic region? If
yes, find the region.
c. Based on your answer to (b), sketch a graph of two isoquants
Q1 and Q2 withQ1 < Q2.
1. (12 points) Consider the production function Q = KL2-L", and answer the following questions. a. (4 pts) Does this production function exhibit diminishing marginal product of capital? Diminishing marginal product of labor? Explain.
Consider the Leontief production function F(KL) = min {K,L], where capital K and labor L have respective positive input prices r and w. (a) Why is it that the cost-minimizing firm sets K 5. L? (b) What is the cost function? (c) How would your answer to part (b) change, if at all, if rw 0? Explain.
1. A production function is given by f(K, L) = L/2+ v K. Given this form, MPL = 1/2 and MPK-2 K (a) Are there constant returns to scale, decreasing returns to scale, or increasing returns to scale? (b) In the short run, capital is fixed at -4 while labor is variable. On the same graph, draw the 2. A production function is f(LK)-(L" + Ka)", where a > 0 and b > 0, For what values of a and...
The three isoquants in the graph below refer to production levels of 100 (red), 200 (green), and 255 (blue). As long as the quantity of capital (K) and labor (L) used in the production process lies on the line a, whenever L is tripled K is also tripled. - =100 =200 - =255 L OPTIONS BELOW a Does this production function exhibit increasing, decreasing, or Increasing constant returns to scale? Decreasing Constant Not enough Information OPTIONS BELOW b Iftold you...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w., and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p. 11. Consider the production function: f(KL)=K+L. Let w and r denote the price of labor and capital, and...
7. Suppose a firm's production function is Q-min(L,K). (This means the level of O produced is the smaller of L and K) a. Graph some isoquants for this firm. b. Let w = 2, r= 1, and suppose the firm's expenditures are C-12. What are the firm's demands for L and K? What is the share of labor in the cost of output? c. Now let w rise to 3. What are the firm's new demands for L and K?...
2. Consider a firm producing pizza with production function q = KL, that faces input prices w= $10 and r = $100 for labor and capital, respectively. a. Derive the isoquant equation. Find the isoquant of an output q = 1. Draw it in a figure with l in the horizontal axis and k in the vertical axis. b. Does this firm's production exhibit increasing, decreasing or constant returns to scale? Briefly explain c. Find the labor demand, and the...
8. Suppose that the following graph shows a few of the isoquants for a firm's production function for producing park benches. The firm's production function is Q = 20KVL. Suppose that the firm's goal is to produce Q= 160 in the cost minimizing way. The cost of a unit of capital (K) is $32 (r=$32) and the cost of a unit of labor is $32 (w=$32). a. Show the firm's cost minimizing isocost on the graph when the firm is...
4. Consider the production functions given below: a. Suppose that the production function faced by a milk producer is given by Q = 40.5 20.5 = 4VK VL, where MPx = 2K-0.5 20.5 = 2 and MP, = 2 K0.5L-05 = 2 * i. Do both labor and capital display diminishing marginal products in the short run? ii. Find the marginal rate of technical substitution for this production function. (Hint: The MRTS = 1) iii. Does this production function display...
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