Suppose the production function is Cobb-Douglas and f(x1, x2) = x^1/2 x^3/2
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Suppose the production function is Cobb-Douglas and f(x1, x2) =
x^1/2 x^3/2
(e) What's the technical...
1. Suppose the production function is Cobb-Douglas and f(11,12) = 21222 (a) Write an expression for...
1. Suppose the production function is Cobb-Douglas and f(11,12) = 21222 (a) Write an expression for the marginal product of 21 at the point (21,12). (b) Holding 22 fixed, for small increases in I, will the marginal product of 2 increase, decrease or remain constant? (c) What's the marginal product of factor 2? Will it increase, remain constant or decrease for small increases in ra? (d) Does an increase in the amount of 22 increase, leave unchanged or decrease the...
Please show all your work step by step 1. Suppose the production function is Cobb-Douglas and f(x1,22) = x122. (...
Please show all your work step by step
1. Suppose the production function is Cobb-Douglas and f(x1,22) = x122. (a) Write an expression for the marginal product of xy at the point (21,22). (b) Holding a fixed, for small increases in 31, will the marginal product of increase, decrease or remain constant? (c) What's the marginal product of factor 2? Will it increase, remain constant or decrease for small increases in x2? (d) Does an increase in the amount of...
Question-3 (Marginal Products and Returns to Scale) (30 points) Suppose the production function is Cobb-Douglas and...
Question-3 (Marginal Products and Returns to Scale) (30 points)
Suppose the production function is Cobb-Douglas and f(x1; x2) =
x1^1/2 x2^3/2
1. Write an expression for the marginal product of x1.
2. Does marginal product of x1 increase for small increases in
x1, holding x2 fixed? Explain
3. Does an increase in the amount of x2 lead to decrease in the
marginal product of x1? Explain
4. What is the technical rate of substitution between x2 and
x1?
5. What...
Douglas production function F(x,, x)- xg, where X1, xl are Consider the Cobb- values of generic...
Douglas production function F(x,, x)- xg, where X1, xl are Consider the Cobb- values of generic inputs, while α marginal product of input i? For any i, for what parameter values is there diminishing marginal product of inpu increasing, constant, and decreasing returns to scale? While a general answer is preferable, you can answer these questions for 1-3. 2. a, are constant nt parameters. Forthe , t i? Under what parameter values does the production fu
Question 2: Production Function and Profit Maxi- mization Consider a production function of Cobb-Douglas form: for...
Question 2: Production Function and Profit Maxi- mization Consider a production function of Cobb-Douglas form: for some α, β E (0, 1) (a) Plot the isoquant of F (b) Derive that technical rate of substitution of F. Does F exhibit diminishing technical rate of substitution? (c) Does F exhibit diminishing marginal productivity of labor? What about marginal (d) Find out the conditions for α and β such that F is increasing return to scale, (e) Suppose that F does not...
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%?
Problem 4: A firm has the following production function: Xi , X2)=X1 , X2 A) Does this firm's tec...
Problem 4: A firm has the following production function: Xi , X2)=X1 , X2 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) What is the firm's Technical Rate of Substitution? What is the optimality condition that determines the firm's optimal level of inputs? C) Is the marginal product of input 1 increasing, constant, or decreasing in x1. Is the marginal product of input 2 increasing, constant, or decreasing in x2? D) Suppose the firm...
A firm uses two inputs x1 and x2 to produce output y. The production function is...
A firm uses two inputs x1 and x2 to produce
output y. The production function is given by f(x1, x2) = p
min{2x1, x2}. The price of input 1 is 1 and the price of input 2 is
2. The price of output is 10.
4. A firm uses two inputs 21 and 22 to produce output y. The production function is given by f(x1, x2) = V min{2x1, x2}. The price of input 1 is 1 and the price...
Problem 3: A firm has the following production function: f(x1,x2) = x7/3x4/3 A) Does this firm's...
Problem 3: A firm has the following production function: f(x1,x2) = x7/3x4/3 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) What is the firm's Technical Rate of Substitution? What is the optimality condition that determines the firm's optimal level of inputs? C) Is the marginal product of input 1 increasing, constant, or decreasing in X1. Is the marginal product of input 2 increasing, constant, or decreasing in xz? D) Suppose the firm wants to...
1. Suppose the production function is Cobb-Douglas and f(11,12) = 21222 (a) Write an expression for the marginal product of 21 at the point (21,12). (b) Holding 22 fixed, for small increases in I, will the marginal product of 2 increase, decrease or remain constant? (c) What's the marginal product of factor 2? Will it increase, remain constant or decrease for small increases in ra? (d) Does an increase in the amount of 22 increase, leave unchanged or decrease the...
Please show all your work step by step
1. Suppose the production function is Cobb-Douglas and f(x1,22) = x122. (a) Write an expression for the marginal product of xy at the point (21,22). (b) Holding a fixed, for small increases in 31, will the marginal product of increase, decrease or remain constant? (c) What's the marginal product of factor 2? Will it increase, remain constant or decrease for small increases in x2? (d) Does an increase in the amount of...
Question-3 (Marginal Products and Returns to Scale) (30 points)
Suppose the production function is Cobb-Douglas and f(x1; x2) =
x1^1/2 x2^3/2
1. Write an expression for the marginal product of x1.
2. Does marginal product of x1 increase for small increases in
x1, holding x2 fixed? Explain
3. Does an increase in the amount of x2 lead to decrease in the
marginal product of x1? Explain
4. What is the technical rate of substitution between x2 and
x1?
5. What...
Douglas production function F(x,, x)- xg, where X1, xl are Consider the Cobb- values of generic inputs, while α marginal product of input i? For any i, for what parameter values is there diminishing marginal product of inpu increasing, constant, and decreasing returns to scale? While a general answer is preferable, you can answer these questions for 1-3. 2. a, are constant nt parameters. Forthe , t i? Under what parameter values does the production fu
Question 2: Production Function and Profit Maxi- mization Consider a production function of Cobb-Douglas form: for some α, β E (0, 1) (a) Plot the isoquant of F (b) Derive that technical rate of substitution of F. Does F exhibit diminishing technical rate of substitution? (c) Does F exhibit diminishing marginal productivity of labor? What about marginal (d) Find out the conditions for α and β such that F is increasing return to scale, (e) Suppose that F does not...
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%?
Problem 4: A firm has the following production function: Xi , X2)=X1 , X2 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) What is the firm's Technical Rate of Substitution? What is the optimality condition that determines the firm's optimal level of inputs? C) Is the marginal product of input 1 increasing, constant, or decreasing in x1. Is the marginal product of input 2 increasing, constant, or decreasing in x2? D) Suppose the firm...
A firm uses two inputs x1 and x2 to produce
output y. The production function is given by f(x1, x2) = p
min{2x1, x2}. The price of input 1 is 1 and the price of input 2 is
2. The price of output is 10.
4. A firm uses two inputs 21 and 22 to produce output y. The production function is given by f(x1, x2) = V min{2x1, x2}. The price of input 1 is 1 and the price...
Problem 3: A firm has the following production function: f(x1,x2) = x7/3x4/3 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) What is the firm's Technical Rate of Substitution? What is the optimality condition that determines the firm's optimal level of inputs? C) Is the marginal product of input 1 increasing, constant, or decreasing in X1. Is the marginal product of input 2 increasing, constant, or decreasing in xz? D) Suppose the firm wants to...
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