1. Suppose the production function is Cobb-Douglas and f(11,12) = 21222 (a) Write an expression for...
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...
Suppose the production function is Cobb-Douglas and f(x1, x2) = x^1/2 x^3/2 (e) What's the technical rate of substitution TRS (11, 12)? (f) Does this technology have diminishing technical rate of substitution? (g) Does this technology demonstrate increasing, constant or decreasing returns to scale?
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...
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%?
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
In a Cobb Douglas production function the marginal product of labor will increase if: a. the quantity of labor increases. b. the quantity of capital increases. c. capital's share of output increases. d. average labor productivity decreases.
Assume a Cobb-Douglas production function F(KL) = Kal1-a with 0 < x < 1, which means f(k) = k«. (f) [4 marks] Does the saving rate SGR needed for the Golden rule rise, remain the same, or fall when climate change increases 8? Explain your argument.
Assume a Cobb-Douglas function such that ? where A=1, K=20, L=16, , and ?. Calculate Q. Does the function show increasing, decreasing, or constant returns to scale? Why? Calculate the marginal produce of K and L. Let K increase to 21 ceteris paribus and calculate the marginal product of K and L. Explain the results. Q = ᎪK L°