Production functions

(a) State whether the following production functions exhibit increasing, constant, or decreasing returns to scale in K and L. Explain each case. (i) Y = AK1/3 L1/2 (ii) Y = AK2/3 L (iii) Y = AK1/2L1/2 (b) Consider the Production model in Table 4.3 below. a is capital share to total output, yo is observed per capita real GDP, ko is observed capital per unit of labour, yp is predicted per capita real GDP as per production model and Ais productivity parameter. Fill in the missing cells. Table 4.3: Production Function Model (U.S. = 1) a yo ko yP = ka A Burundi 0.39 0.02 0.01 Text Text Brazil 0.44 0.29 0.40 Switzerland 0.35 1.21 1.40 China 0.43 0.24 0.31 Spain 0.42 0.63 1.10 United Kingdom 0.39 0.75 1.11 Croatia 0.33 0.40 0.58 India 0.50 0.10 0.10 BACK TO TOP (Source: Penn World Tables 9.0) O a e P ENG 2:00 PM 9/06/2020 73