Homework Answers
Please show clear work. , ifĀ = 2,Ī = 4 3. (24 pts) Solow Model: Given...
Please show clear work.
, ifĀ = 2,Ī = 4 3. (24 pts) Solow Model: Given a production function Y; = AKSZ ,s= 0.2, and d = 0.05, a. (6 pts) set up the steady-state condition, then plug in the above values for parameters, and finally show your work to calculate the steady-state level of capital b. (6 pts) calculate the steady-state level of production C. (6 pts) Does the above production function exhibit constant returns to scale? Explain, including...
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP...
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP + bK°]!/p where p a. Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) b. What are the returns to scale for this production function? Show and explain. Explain what will happen to cost if the firm doubles its...
the second question In Example 6.4 wheat is produced according to the production function: q=100(k0.6 0.4)...
the second question
In Example 6.4 wheat is produced according to the production function: q=100(k0.6 0.4) Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing (Round responses to two decimal places.) The MPK at 5 units of capital is 156.12 The MP at 6 units of capital is 144.02 The MP at 50 units of labor is 8.84 The MP...
Question 2 130 marks] Suppose that the production function is given by Y 0.5VKv/N. Assume that...
Question 2 130 marks] Suppose that the production function is given by Y 0.5VKv/N. Assume that the size of the population, the labour participation rate and the unemployment rate are all constant. a) Does this production function exhibit constant returns to scale? Explain (5 marks) b) Explain the difference between returns to factors of production and returns to scale (4 marks) cTransform the production function into a relationship between output per worker and capital per worker. (5 marks) d) Assume...
Consider the production function below. ?? ?(?, ?) = ?? + ?? a) Find the demand...
Consider the production function below. ?? ?(?, ?) = ?? + ?? a) Find the demand for labor and capital b) Draw the demand curve for labor c) Does the production function exhibit diminishing marginal returns of labor? d) Is the production function exhibiting increasing, constant or decreasing returns to scale?
Suppose the production function is given as ? = √??. Suppose also that the price of...
Suppose the production function is given as ? = √??. Suppose also that the price of labor ? = 10 and the price of capital ? = 40 1) Derive the equation of the isoquant corresponding to this production function? 2) What type of return to scale does this production exhibit? 3) Does this production function exhibit a diminishing MRTS? Why? 4) Based on this production function, is the law of diminishing marginal returns satisfied? 5) Derive the demand curves...
Suppose the production function is given as Q = VLK. Suppose also that the price of...
Suppose the production function is given as Q = VLK. Suppose also that the price of labor w = 10 and the price of capital r = 40 1) Derive the equation of the isoquant corresponding to this production function? 2) What type of return to scale does this production exhibit? 3) Does this production function exhibit a diminishing MRTS? Why? 4) Based on this production function, is the law of diminishing marginal returns satisfied? 5) Derive the demand curves...
Consider a firm that has the following CES production function: Q = f(L,K) = [aL^ρ + bK^ρ]^1/ρ where ρ ≤ 1. Please...
Consider a firm that has the following CES production function: Q = f(L,K) = [aL^ρ + bK^ρ]^1/ρ where ρ ≤ 1. Please clearly show each STEP and make sure your handwriting is LEGABLE. Thank you Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) What are the returns to scale for this production function? Show...
2. A different firm has this daily production function. Assume that capital is fixed at 8...
2. A different firm has this daily production function. Assume that capital is fixed at 8 units. q K1312/3 a. Give the marginal product function. (Write and circle your answer.) b. Give the derivative of the marginal product function. (Write and circle your answer.) c. Is the production function concave or convex? (Write and circle your answer.) Does this production function exhibit diminishing marginal product for labor? (Write "yes" or "no" and circle your answer.) d. Which best describes this...
For each of the following production functions, solve for the marginal products of each input and marginal rate of substitution.
For each of the following production functions, solve for the marginal products of each input and marginal rate of substitution. Then answer the following for each: does this production function exhibit diminishing marginal product of labour? Does this production function exhibit diminishing marginal product of capital? Does this production function exhibit constant, decreasing, or increasing returns to scale? Show all your work.(a) \(Q=L+K\)(b) \(Q=2 L^{2}+K^{2}\)(c) \(Q=L^{1 / 2} K^{1 / 2}\)
Please show clear work.
, ifĀ = 2,Ī = 4 3. (24 pts) Solow Model: Given a production function Y; = AKSZ ,s= 0.2, and d = 0.05, a. (6 pts) set up the steady-state condition, then plug in the above values for parameters, and finally show your work to calculate the steady-state level of capital b. (6 pts) calculate the steady-state level of production C. (6 pts) Does the above production function exhibit constant returns to scale? Explain, including...
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP + bK°]!/p where p a. Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) b. What are the returns to scale for this production function? Show and explain. Explain what will happen to cost if the firm doubles its...
the second question
In Example 6.4 wheat is produced according to the production function: q=100(k0.6 0.4) Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing (Round responses to two decimal places.) The MPK at 5 units of capital is 156.12 The MP at 6 units of capital is 144.02 The MP at 50 units of labor is 8.84 The MP...
Question 2 130 marks] Suppose that the production function is given by Y 0.5VKv/N. Assume that the size of the population, the labour participation rate and the unemployment rate are all constant. a) Does this production function exhibit constant returns to scale? Explain (5 marks) b) Explain the difference between returns to factors of production and returns to scale (4 marks) cTransform the production function into a relationship between output per worker and capital per worker. (5 marks) d) Assume...
Suppose the production function is given as Q = VLK. Suppose also that the price of labor w = 10 and the price of capital r = 40 1) Derive the equation of the isoquant corresponding to this production function? 2) What type of return to scale does this production exhibit? 3) Does this production function exhibit a diminishing MRTS? Why? 4) Based on this production function, is the law of diminishing marginal returns satisfied? 5) Derive the demand curves...
2. A different firm has this daily production function. Assume that capital is fixed at 8 units. q K1312/3 a. Give the marginal product function. (Write and circle your answer.) b. Give the derivative of the marginal product function. (Write and circle your answer.) c. Is the production function concave or convex? (Write and circle your answer.) Does this production function exhibit diminishing marginal product for labor? (Write "yes" or "no" and circle your answer.) d. Which best describes this...
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