. Consider the following production function: Q = Km characteristics of this pro

Question

. Consider the following production function: Q = Km characteristics of this production function. How is it different from a Linear production function? How is it different from a Leontief production function? (8 marks) Assuming that the firm hires 10 units of capital and 20 units of labour, use the production function given in part a to compute the average and marginal products of labour. (8 marks) Explain how the firm would use the marginal product of labour to determine the profit maximizing quantity of labour which the firm would hire (4 marks) 1. Explain the special a. b. c.

Explanation / Answer

Answer

a)

Q = K2/3L1/3

i) This is a Cobb Douglas Production Function.

ii) This Production Function exhibit Constant Return to scale as:

Q(tK,tL) = t K2/3L1/3 = tQ(K,L)

iii) Elasticity Of substitution for this production function is 1 i.e.,

(percentage change in K/L)/(percentage change in MRTS) = 1

iv) As the equation suggest it is a convex function

v) MRTS is diminishing

Cobb Douglas Vs Linear function

i) The function mentioned is Cobb douglas while linear function is a perfect substitute case

ii) MRTS of given function is diminishing while MRTS of linear function is constant

iii)Elasticity Of substitution of function given is 1 while elasticity of substitution for Linear production function is infinity.

Q=K2/3L1/3 Vs leontieff Production Function

i) The function mentioned is convex while leontieff Production Function is L shaped curve

ii) MRTS of given function is diminishing while MRTS of linear function is 0 and infinity

iii)Elasticity Of substitution of function given is 1 while elasticity of substitution for leontieff Production Function is Zero.

b)

MPL = del(Q)/del(L) = Partial differenctiation of Q with respect to L

= (1/3)(K/L)2/3

= (1/3)*(1/2)2/3

  = 0.08

APL = Outpul per Unit Labour

= Q/L = 102/3201/3

= 12.6/20

= 0.63

c)

For profit maximization We have to maximize the following as Profit = Total Revenue -Total Cost. Hence:

Profit = P*(K2/3L1/3) - TC = P*(K2/3L1/3) - vk + wL

where w = wage rate and v = rate of capital and P is price of the product

hence

Using First Order Condition we have

del(P*(K2/3L1/3) )/del(L) - w = 0

and del(P*(K2/3L1/3))/del(k) - v = 0

so MPL = w/P

and MPK = v/P

Hence,

Firms Use above equations to determine profit maximizing quantity of Labour and Capital.

To determine profit maximizing quantity of labour and Capital, firms has to determine L and K, such that MPL = w/P and MPK = v/P

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.