Question

please use computer to do this question ( I do not understand hand writing)

4. Determine if the following production technologies exhibit IRS, DRS, or CRS, and explain why. (1 point each)

      a. q=2KL

      b. q=5KL

      c. q=

      d. q=

      e. q=K+L

      f. q=3K+3L

      g.q=8(K+L)

Answer 1

To find returns to scale,

first we multiply the inputs ie, K and L with a constant, if the output come out to be same no. with power 1- it means production technologies exhibit Constant returns to scale ( CRS)

-if the output come out to be same no. with power more than 1- it means production technologies exhibit Increasing returns to scale ( IRS)

- if the output come out to be same no. with power less than 1- it means production technologies exhibit decreasing returns to scale ( DRS).

a) q(K,L) = 2KL

q( tk, tL) = 2(tK)(tL) = 2t² KL

q( tk, tL) = t² *2KL

q( tk, tL) = t² *q(K,L)

As power of t is more than 1, the production technologies exhibit IRS.

b) q(K,L) = 5KL

q( tk, tL) = 5(tK)(tL) = 5t² KL

q( tk, tL) = t² *5KL

q( tk, tL) = t² *q(K,L)

As power of t is more than 1, the production technologies exhibit IRS.

c) q=K^(1/2) L^(1/2)

q( K,L) = K^1/2 L^1/2

q(tK, tL) = (tK)^1/2 (tL)^1/2

q(tK, tL) = t(K^1/2 L^1/2)

q(tK, tL) = t*q(K,L)

As power of t = 1, so production function exhibits constant returns to scale.

d. q=K^(1/3) L^(1/3)

q=K^(1/2) L^(1/2)

q( K,L) = K^1/3 L^1/3

q(tK, tL) = (tK)^1/3 (tL)^1/3

q(tK, tL) = t^{1/3+ 1/3}(K^1/2 L^1/2)

q(tK, tL) = t^2/3*q(K,L)

As power of t is less than 1 ( 2/3= 0.66), so production function exhibits decreasing returns to scale.

e) q(K,L) = K + L

q( tk, tL) = (tK) + (tL)

q( tk, tL) = t( K + L)

q( tk, tL) = t *q(K,L)

As power of t is equal to 1, the production technologies exhibit CRS.

f)

q(K,L) = 3K + 3L

q( tk, tL) = 3(tK) + 3(tL)

q( tk, tL) = t( 3K + 3L)

q( tk, tL) = t *q(K,L)

As power of t is equal to 1, the production technologies exhibit CRS.

g)

q(K,L) = 8(K + L)

q( tk, tL) = 8((tK) + (tL))

q( tk, tL) = t*8( K + L)

q( tk, tL) = t *q(K,L)

As power of t is equal to 1, the production technologies exhibit CRS.