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).
3. A company has a production function with three inputs x, y and z, given by 2 1 1 f(x, y, z)=50x/5 y 5; 5. The total budget is $24,000 and the company can buy x, y and z at $80, $12 and $10 per unit respectively. What combination of inputs will maximize production? [12 ma 0- K 5C X
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)...
Consider a production function Q = 3K + 4L, when L is graphed on the x-axis and K is graphed on the y-axis, the marginal rate of technical substitution is equal to A) 4/3 and the isoquant is convex to the origin. B) 4/3 and the isoquant is a straight line. C) and the isoquant is a straight line. D) 12 and the isoquant is convex to the origin.
If z=sin(x/y) , x=3t , y=5−t^2 dz/dt using the chain rule. Assume the variables are restricted to domains on which the functions are defined. dz/dt=
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...
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...
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 -...
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...