(a) For the cost function C(w₁, W2, y) 2y ww, calculate the Allen elasticity of substitution between the two inputs at the cost-minimizing input point (ri(w₁, W2, y), x(w₁, W2, y)). = (b) Consider the production function f(x, y, z) = √ry+xz+yz. Find the scale elasticity SE at (x, y, z) = (1, 2, 3), (5, 1, 6), (6, 6, 6) and determine if the pro- duction function is IRTS, CRTS, or DRTS locally at each point. (c) A profit maximizing firm in the market operates where the production exhibits decreasing return to scale (DRTS). Is this market in its long-run equilibrium? Justify your answer

(a) For the cost function C(w₁, W2, y) 2y ww, calculate the Allen elasticity of substitution between the two inputs at the cost-minimizing input point (ri(w₁, W2, y), x(w₁, W2, y)). = (b) Consider the production function f(x, y, z) = √ry+xz+yz. Find the scale elasticity SE at (x, y, z) = (1, 2, 3), (5, 1, 6), (6, 6, 6) and determine if the pro- duction function is IRTS, CRTS, or DRTS locally at each point. (c) A profit maximizing firm in the market operates where the production exhibits decreasing return to scale (DRTS). Is this market in its long-run equilibrium? Justify your answer

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.7P

See similar textbooks

Similar questions

What is AC(y) for cost function c(y) = y3? Input prices are taken as constants.
*Find the elasticity of scale and the elasticity of substitution for the CES production function f(x1,x2) = (x{ + x%)¯,where 0 #p<1.
E. A firm has the production function f(T1, 12) = 1750 , 50 What is the marginal rate of technical substitution (M RTS)? (a) MRTS =-1 2.5x, (b) MRTS = -x2/x1 (c) MRTS = -5x2/01 (d) MRTS =-0.5x2/21 (e) MRTS = -0.2x2/21 %3D %3D
What is MC(y) for cost function c(y) = y3? Input prices are taken as constants.
: Suppose that the production functions be like as (A) i) Y = X15 X20.5 ii)Y= X10.5 + X20.5 Find MRTS of these functions
What is the elasticity of substitution for the production function f(K, L) = K¹/4 [³/4? (a) o = 1 (b) o = -1 (c) o = 1 (d) σ = 3 2
Compute the MRTS for this production function: Y (K,L) = 2K+5L
a= min[x,y]^(1/2) a)Draw isoquants for a = 1, a = 4 and a = 9. b)What kind of returns to scale does the production function have? c)The price of x is p_x = 1 and of y p_y = 2. Calculate the cost function. d)Rent is $ 400, calculate average and marginal costs.
please analyze the behavior of cost function and interpret the constant term in the expression of C(q)
1. Find the cost minimizing input demand functions (x¿(w,q)) and the cost function (c(w,q)) for the following production functions: 1/3 21382 a. f(x) = x₁
A factory makes bicycle tires. The cost, C, in dollars and revenuue in dollars, R, are both functions of the number of tires, n.a) Describe what is meant by C'(4) = 8b) Generate a mathematical equation, using function notation, to model the following statements: for (b) + (c) "The marginal revune for 15 tires sold decreases by $1."c) "The revenue at 3 tires equals the change in cost at 5 tires"