. Discuss about returns to scale of following production function. (a) f(x1, x2) = x a 1 +x a 2 b , where a and b are positive constant. (Hint: ab < 1, ab = 1 and ab > 1.) (b) f(x1, x2) = √ x1 + x 2 2 . (Hint: Does it satisfy the definition of increasing return to scale, constant returns to scale, or decreasing returns to scale. How can this be?)
1. F(x1,x2) = x1ab + x2ab
F(kx1,kx2) = kab(x1ab + x2ab) = kab(F(x1,x2))
For ab = 1, the production function has Constant Returns to Scale.
For ab < 1, the production function has Decreasing Returns to Scale.
For ab > 1, the production function has Increasing Returns to Scale.
This production function has Constant Returns to Scale.
2. F(x1,x2) = + x2
F(kx1,kx2) = * + kx2 < k( + x2) = F(x1,x2) for k > 1. Hence, for k > 1, this production function has decreasing returns to scale.
. Discuss about returns to scale of following production function. (a) f(x1, x2) = x a...
Problem 2: A firm has the following production function: f(x1,x2) = x1 + x2 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) Suppose the firm wants to produce exactly y units and that input 1 costs $w1 per unit and input 2 costs $w2 per unit. What are the firm's conditional input demand functions? C) Write down the formula for the firm's total cost function as a function of w1, W2, and y.
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...
1a) A production function has the form f(a,b) = a^2 x b^3 . Does this function exhibit constant, increasing, or decreasing returns to scale? 1b)A production function has the form f(a,b) = 3a^1/2 x b^1/2. Does this function exhibit constant, increasing, or decreasing returns to scale? Explain. Thank you.
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...
Returns to scale. A production function has constant returns to scale with respect to inputs with inputs K and L if for any z > 0: F(z · K, z ·L) = zF(K, L), For example, for a production function with constant returns to scale, doubling the amount of each input (i.e., setting z = 2) will lead to a doubling of the output from the production function. A production function has increasing returns to scale if for any z >1: F(z ·...
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...
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
Prove that the production function f(X1, X2, X3) = 29X1aX2bX3c, where a + b + c > 1, has increasing returns to scale.