Production is given by
p(x, y) = 10x(y^2) + x^2
inputs are restricted by
x=(z^3) and y=(2z^2)
using the chain rule what is the production rate of change when z=1?
What is the isoquant and marginal rate of technical substitution when x=2 and y=3.
Production is given by p(x, y) = 10x(y^2) + x^2 inputs are restricted by x=(z^3) and...
3. Consider the following production function with two inputs X1 and x2. y = alnx + Blny a. Derive the equation for an isoquant (assuming x is on the y-axis). b. Derive the marginal product of input x. c. Derive the marginal product of input x. d. Derive the marginal rate pf technical substitution (MRTS).
2. Consider the following production function with two inputs X1 and X2. y = x1/2x2/4 a. Derive the equation for an isoquant (assuming X2 is on the y-axis). b. Derive the marginal product of input x1. c. Derive the marginal product of input x2. d. Derive the marginal rate pf technical substitution (MRTS).
TUTORIAL2 Chapter 7 Part 1 Key Concepts and Equations: Production Isoquant: shows all combinations of input quantities that yield the same level of output. Higher isoquant: higher level of output Marginal Rate of Technical Substitution: MRTS is the slope of the isoquant at any input combination. It tells us the rate at which we must increase the qty of input 2 per unit decrease in qty of input 1. MRTS diminishes as we move down the isoquant from left to...
3. Let q = Lākā denote the production function for a firm making long-run decisions, that is K (capital) and L (labor) are now variable. a. Place k on the Y-axis and L on the X-axis and illustrate an isoquant when q=100. b. Derive an expression for the MRTS (the marginal rate of technical substitution) for any level of q.
Consider the function f(x,y,z) =63 - 26 x y z - 8 y^2z + 76 x^4+ 18 y^4- 31 yz^3.Find (a) the greatest rate of change of f atP[0]=(19, 13, 4), and (b) the UNIT vector that points inthe direction of greatest rate of change of f atP[0]
Given production function: y=f(x1,x2)=(α⋅x(σ−1)/σ1+(1−α)⋅x(σ−1)/σ2)σ/(σ−1) consider, α = 0.2 and σ = 0.7. The first factor is currently used in the amount x1 = 9, and the second factor is used in the amount x2 = 3. a) When (x1,x2) = (9,3), how much output is being produced? Output: b) When (x1,x2) = (9,3), what is the marginal product of factor 1? Marginal product: c) When (x1,x2) = (9,3), what is the average product of factor 1? Average product: d) When...
a - e (a) X + y +z = 11 X – Y – 2= -3 -2 + y - 2 = 5 (3x – y + 2z = 2 (b) x+y+z+t+p=17 X - Y - 2-t-p= -5 z +t+ p + y = 11 p - x - y = 1 -t + x = 10 (c) x +y + 2+t= -6 X - Y - 2 -t = 20 y - X=-39 2x + 3t + y -...
Find the directional derivative of the function f(x,y,z) = -67 y^2z + 8 z^2- 48 x^2y z - 25 x y^2z+ 93 x^4yat the pointP[0]= (6, -14, -7) inthe direction fromP[0]to the pointP[1]=(14, 3, 16)
TUTORIAL2 Chapter 7 Part 1 Key Concepts and Equations: Production Isoquant: shows all combinations of input quantities that yield the same level of output. Higher isoquant: higher level of output Marginal Rate of Technical Substitution: MRTS is the slope of the isoquant at any input combination. It tells us the rate at which we must increase the qty of input 2 per unit decrease in qty of input 1. MRTS diminishes as we move down the isoquant from left to...
4. Consider the production functions given below: a. Suppose that the production function faced by a milk producer is given by Q = 40.5 20.5 = 4VK VL, where MPx = 2K-0.5 20.5 = 2 and MP, = 2 K0.5L-05 = 2 * i. Do both labor and capital display diminishing marginal products in the short run? ii. Find the marginal rate of technical substitution for this production function. (Hint: The MRTS = 1) iii. Does this production function display...
Post an Article
Post an Answer
Post a Question
with Answer
Self-promotion: Authors have the chance of a link back to their own personal blogs or social media profile pages.