
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)
The production function is f(K,L)=K(1/2)+L(1/2) for questions 4, 5, and bonus. 4. Does this production function exhibit decreasing, constant, or increasing returns to scale. 5. Find the rate of technical substitution. Bonus. Find the elasticity of substitution (σ) for this production function.
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...