7. For the production function y = f (2,.., ) = (Žaix}" y = f(21,..., with...
Question 5 (20 marks) (a) i) A firm has production function y - f(x,z) -ax+Bz, for y 2 0, where y is output, and x, z the factors of production. Are the returns to scale constant, increasing or decreasing? Explain your answer. (3 marks) ii) Consider the production function: f(x1,2)2 where a is a positive parame- ter. Indicate for which values of a the returns to scale in production are increasing Explain your answer. (3 marks) iii) A firm has...
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...
1. Suppose that output is generated by the production function Y = F(K, L, M = AK1-0-BL M. where M is the quantity of raw materials used in production. What condition is necessary for the production function to exhibit constant returns to scale? 2. Suppose instead that output is generated by a "constant elasticity of substitution" (CES) production function, Y = F(K,L) = A(Kº + L), where a < 1. What condition is necessary for the CES production function to...
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is the output, L is the labour input, and K is the capital input. (a) Does this exhibit constant, increasing, or decreasing returns to scale? (b) Suppose that the firm employs 9 units of capital, and in the short-run, it cannot change this amount. Then what is the short-run production function? (c) Determine whether the short-run production function exhibits diminishing marginal product of labour. (d)...
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.
6. Consider the following Cobb - Douglas utility function: U = xayBzY *Note, it should be assumed that a, B.y > 0 Show that this production function can exhibit increasing returns to scale globally while maintaining diminishing returns for each individual input.
Determine the value of such that the function f (x, y) = cxy for 0<x<3 and 0 <y<3 satisfies the properties of a joint probability density function. Determine the following. Round your answers to four decimal places (e.g. 98.7654). 1.0994 P&<2,Y<3) 7.4444 P(X<2.0) 21:1878 Pu<Y<1,7) 12489 P(X>1.8,1 <Y<2.5) 7:3733 EX) P(X < 0,8< 4)
Suppose the firm's production function is given by f(K,L) = min {K",L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive
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...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...