Question

5.5 We estimated that BlackBerry’s production function is ? = 2.83? ? , where L is labor and K is

capital. Epple et al. (2010) estimated that the production function for U.S. housing is ? =0.144 0.856

1.38? ? , where L is land and M is an aggregate of all other mobile, nonland factors, which we call materials. Haskel and Sadun (2012) estimated that the production function for U.K. supermarkets is

0.23 0.10 0.66
? = ? ? ? , where L is labor, K is capital, and M is materials. Do each of these production

functions have decreasing, constant, or increasing returns to scale? (Hint: See Solved Problem 6.3.)

This is from the Person Microeconomics 8th edition textbook by Perloff

Answer 1

Answer

A function exhibit increasing returns to scale if f(tx,ty,tz) > t*f(x,y,z) for all t > 1

BLACKBERRY'S PRODUCTION FUNCTION

Here, f(K,L) = 2.83LK => f(tK,tL) = 2.83(tL)(tK) = t2(2.83LK) > t(2.83LK) = t*f(L,K)

=> f(tK,tL) > t*f(K,L) for all t > 1.

Hence this function exhibit increasing returns to scale.

EPPEL'S PRODUCTION FUNCTION

A function exhibit constant returns to scale if f(tx,ty,tz) = t*f(x,y,z) for all t > 1

Here, f(L,M) = 1.38L0.144M0.856 => f(tL,tM) = 1.38(tL)0.144(tM)0.856 = t(1.38L0.144M0.856) = t*f(L,M)

=> f(tL,tM) = t*f(L,M) for all t > 1.

Hence this function exhibit constant returns to scale.

HASKEL'S PRODUCTION FUNCTION

A function exhibit decreasing returns to scale if f(tx,ty,tz) < t*f(x,y,z) for all t > 1

Here, f(K,L,M) = L0.23K0.10M0.66 => f(tK,tL,tM) = (tL)0.23(tK)0.10(tM)0.66 = t0.99(L0.144M0.856) < t*f(K,L,M)

=> f(tK,tL,tM) < t*f(K,L,M) for all t > 1.

Hence this function exhibit constant decreasing to scale.