Question

Question-3 (Marginal Products and Returns to Scale) (30 points) Suppose the production function is Cobb-Douglas and f(x1; x2) = x₁^1/2 x₂^3/2

1. Write an expression for the marginal product of x1.

2. Does marginal product of x1 increase for small increases in x1, holding x2 fixed? Explain

3. Does an increase in the amount of x2 lead to decrease in the marginal product of x1? Explain

4. What is the technical rate of substitution between x2 and x1?

5. What is the type of returns to scale of this production function? (Increasing, decreasing, constant)

Question-3 (Marginal Products and Returns to Scale) (30 points) Suppose the production function is Cobb-Douglas and 1/2 3/2 f(x1; 22) = x1' 22 1. Write an expression for the marginal product of X1. 2. Does marginal product of xı increase for small increases in Xi, holding X2 fixed? Explain 3. Does an increase in the amount of x2 lead to decrease the marginal product of xı? Explain 4. What is the the technical rate of substitution between X2 and xj? 5. What is the type of returns to scale of this production function? (Increasing, decreasing, constant)

Answer 1

flsel, d22) , = 12 312 XI mle = 2f (ser, *2) axel =(x,V2 yeye 312) coser -1/2 3/2 M2 - / sel As al 9 Increases, Marginal Marginal product decrease ho will of holding rel constant x2 14) false, Increase in amount of lead to Increase in prosginal Product of sei MRTS = in) -mbce Mina 1/2 x2 3/2 201 19 112 12 oll 02 3/7 (1/3) X2 xl 19

21 x2 = 112 3/2 flopper) fffxv, t>ca) = (tor) 44 tone)! = + 12 x 1/2 t t floor, ay) Guareasing returns to scale 3/2 3/2 212