Let q = L½k½ denote the production function for a firm making long-run decisions
Let q = L½k½ denote the production function for a firm making long-run decisions, that is K (capital) and L (labor) are now variable.
a. Place k on the Y-axis and L on the X-axis and illustrate an isoquant when q=100.
b. Derive an expression for the MRTS (the marginal rate of technical substitution) for any level of q.
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Let q = L½k½ denote the production function for a firm making long-run decisions
Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor.
Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor. a. Find marginal product of labor and marginal product of capital.b. Define what is marginal rate of technical substitution, MRTS. Calculate the MRTS for the above case.c. When K = 10, L = 16, what is the total output? Sketch this isoquant function on a diagram where K is the vertical axis and L is the horizontal axis.
2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions...
2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?
SHOW ALL WORK!!! 2. For the following Cobb-Douglas production function, q=f(L,K) = _0.45 0.7 a. Derive expressions for m...
SHOW ALL WORK!!!
2. For the following Cobb-Douglas production function, q=f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?
Consider the following Cobb-Douglas production function, where α Find the equation for the isoquant when Q...
Consider the following Cobb-Douglas production function, where α Find the equation for the isoquant when Q 4,000. K-(Properly format your expression using the fools in the paiette. Hover over tools to see keyboard shortcuts Eg, a fraction can be created with the /character) The marginal rate of technical substitution (MRTS) when Q 4,000 and L-50 (with capital measured on the vertical axis and labor measured on the horizontal axis) is MRTS (Enter a numenic response using an integer)
Suppose the production function for a firm is given by: q-2L *4K. If the firm currently...
Suppose the production function for a firm is given by: q-2L *4K. If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTSx) (Round to the nearest fwo decimal places if necessary) Answer Suppose the production function for a firm is given by: q-4L K 25 If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal...
Suppose the production function for automobiles is ? = ?? where Q is the quantity of...
Suppose the production function for automobiles is ? = ?? where Q is the quantity of automobiles produced per year, L is the quantity of labor (man-hours) and K is the quantity of capital (machine hours). a) What is the total product (number of automobiles) if the firm uses 25 man hours and 2 machine hours? b) Sketch the isoquant corresponding to a quantity of Q=50. c) What is the general equation for the isoquant corresponding to any level of...
Suppose the production function for a firm is given by: q=2L +4K. If the firm currently...
Suppose the production function for a firm is given by: q=2L +4K. If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTS). (Round to the nearest two decimal places if necessary.) Answer:
Consider the following Cobb Douglas production function, where =0.5 Q=KLP Find the equation for the isoquant...
Consider the following Cobb Douglas production function, where =0.5 Q=KLP Find the equation for the isoquant when Q=4,000 16.000.000 (Property format your expression using the tools in the palette. Hover over fools to see keyboard shortcuts. Eg, a fraction can be created with the character.) The marginal rate of technical substitution (MRTS) when Q ) 4,000 and L - 100 (with capital measured on the vertical axis and labor measured on the horizontal 2 MRTS - (Enter a numeric response...
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...
0.5,,0.25 Suppose the production function for a firm is given by: q-4L If the firm currently...
0.5,,0.25 Suppose the production function for a firm is given by: q-4L If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTS). (Round to the nearest two decimal places if necessary.) Answer
2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?
SHOW ALL WORK!!!
2. For the following Cobb-Douglas production function, q=f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?
Consider the following Cobb-Douglas production function, where α Find the equation for the isoquant when Q 4,000. K-(Properly format your expression using the fools in the paiette. Hover over tools to see keyboard shortcuts Eg, a fraction can be created with the /character) The marginal rate of technical substitution (MRTS) when Q 4,000 and L-50 (with capital measured on the vertical axis and labor measured on the horizontal axis) is MRTS (Enter a numenic response using an integer)
Suppose the production function for a firm is given by: q-2L *4K. If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTSx) (Round to the nearest fwo decimal places if necessary) Answer Suppose the production function for a firm is given by: q-4L K 25 If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal...
Suppose the production function for a firm is given by: q=2L +4K. If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTS). (Round to the nearest two decimal places if necessary.) Answer:
Consider the following Cobb Douglas production function, where =0.5 Q=KLP Find the equation for the isoquant when Q=4,000 16.000.000 (Property format your expression using the tools in the palette. Hover over fools to see keyboard shortcuts. Eg, a fraction can be created with the character.) The marginal rate of technical substitution (MRTS) when Q ) 4,000 and L - 100 (with capital measured on the vertical axis and labor measured on the horizontal 2 MRTS - (Enter a numeric response...
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...
0.5,,0.25 Suppose the production function for a firm is given by: q-4L If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTS). (Round to the nearest two decimal places if necessary.) Answer
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