Consider a production function of the following form: F(Kt, Nt) = ln(φKt + θln(Nt)) where Kt...
Consider a production function of the following form: F(Kt, Nt) = ln(φKt + θln(Nt)) where Kt is physical capital, Nt is labor hours, and θ,φ are exogenous parameters. Does this production function satisfy basic economic theories? Explain/prove why or why not
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![The production fenation is F (kt, Nt) = in [ukt + ln (NE)] = 4+ MP = 2 = 1 kk + 8 in (Ne)] * * Y+ MP4 = . xe TWKŁ + oln (NU)](http://img.homeworklib.com/questions/1e8e9310-739f-11ea-9c4c-21958f2bdc60.png?x-oss-process=image/resize,w_560)
Here the marginal productivity of both inputs are positive implied both the inputs are positively related to the production function, => as any of these inputs increases the production increases. Now, both the marginal products are negative implied as more and more of additional inputs are added the output increases but at a decreasing rate, => “diminishing marginal productivity” holds. So, the given production function holds all the economic theories.
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Consider a production function of the following form: F(Kt, Nt)
= ln(φKt + θln(Nt)) where Kt...
Consider the Cobb-Douglas production function
Please help with part c. Thank you!Returns to scale Consider the Cobb-Douglas production function, Yt = KẠN L-a=b. This production function includes three inputs: capital (Kt), labor (Nt), and land (Lt). a) Under what conditions does the function exhibit decreasing returns to scale in Kt, Nt and Lt individually? b) Show that the function exhibits constant returns to scale in Kt, Nt and Ljointly. c) Define (lowercase) yt = *, ku = and lt = . Express Yt as a...
Problem 4 Consider the production model in chapter 4. Assume that, in the production function, the...
Problem 4 Consider the production model in chapter 4. Assume that, in the production function, the exponents orn capital and labor are respectively 3/5 and 2/5. a) Write down the equation of the model and mark the endogenous and exogenous variables/parameters How does the firm decide how much labor to hire and capital to rent? Show and explain. What does it mean to solve the model? Solve the model reporting all the steps. What is the equilibrium? Define and report...
14. (Bpts) Consider an agricultural production function Y = F(KL), where is the number of units...
14. (Bpts) Consider an agricultural production function Y = F(KL), where is the number of units produced, Kis capital invested, and Lis labor input. Then Y = dY/dK is called the marginal product of capital. Similarly, Y = dY/dL is the marginal products of labor. (1) (2pts) in economics, what does dY/dK = 5 mean? Explain its economic meaning in words (2) (6pts, 2pts each) if a and b are constants, compute the expression KYK + LY for the following...
1. Consider a steel firm that faces a convex isoquant production function where the inputs are...
1. Consider a steel firm that faces a convex isoquant production function where the inputs are labor and capital. The production function yields constant returns to scale. The firm is currently at a cost-minimizing combination of labor and capital for the desired level of output. Suppose the capital used in the production process emits low amounts of polluted wastewater into a nearby river. In order to promote the use of the environmentally friendly capital the government provides a unit subsidy...
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...
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...
1. (The AK Model) Consider an economy with an aggregate production function given by y =...
1. (The AK Model) Consider an economy with an aggregate production function given by y = F(K) = AK Capital is the only relevant factor of production. A is fixed and represents the productivity of capital. The law of motion for capital is just as in the neoclassical model where s and δ are the savings rate and depreciation rate, respectively. a) Show whether F(K) exhibits constant, decreasing or increasing returns to scale. Com- pute the marginal product of capital....
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.
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and...
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if f-0, the two input Labour and capital are imperfect substitutes in production
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if...
Please help with part c. Thank you!Returns to scale Consider the Cobb-Douglas production function, Yt = KẠN L-a=b. This production function includes three inputs: capital (Kt), labor (Nt), and land (Lt). a) Under what conditions does the function exhibit decreasing returns to scale in Kt, Nt and Lt individually? b) Show that the function exhibits constant returns to scale in Kt, Nt and Ljointly. c) Define (lowercase) yt = *, ku = and lt = . Express Yt as a...
Problem 4 Consider the production model in chapter 4. Assume that, in the production function, the exponents orn capital and labor are respectively 3/5 and 2/5. a) Write down the equation of the model and mark the endogenous and exogenous variables/parameters How does the firm decide how much labor to hire and capital to rent? Show and explain. What does it mean to solve the model? Solve the model reporting all the steps. What is the equilibrium? Define and report...
14. (Bpts) Consider an agricultural production function Y = F(KL), where is the number of units produced, Kis capital invested, and Lis labor input. Then Y = dY/dK is called the marginal product of capital. Similarly, Y = dY/dL is the marginal products of labor. (1) (2pts) in economics, what does dY/dK = 5 mean? Explain its economic meaning in words (2) (6pts, 2pts each) if a and b are constants, compute the expression KYK + LY for the following...
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...
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...
1. (The AK Model) Consider an economy with an aggregate production function given by y = F(K) = AK Capital is the only relevant factor of production. A is fixed and represents the productivity of capital. The law of motion for capital is just as in the neoclassical model where s and δ are the savings rate and depreciation rate, respectively. a) Show whether F(K) exhibits constant, decreasing or increasing returns to scale. Com- pute the marginal product of capital....
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.
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if f-0, the two input Labour and capital are imperfect substitutes in production
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if...
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