Question

Productivity of a Country The productivity of a country in Western Europe is given by the function X,Y) - 40x4/51/5 when x units of labor and y units of capital are used. (a) What are the marginal productivity of labor and the marginal productivity of capital when the amounts expended on labor and capital are 32 units and 1024 units, respectively? (Round your answers to two decimal places.) labor units capital units (b) Should the government encourage capital investment rather the increased expenditure on labor at this time in order to increase the country's productivity? Yes O No Need Help? Read it W atch T alk to a Tutor

Answer 1

a) Consider the productivity function f (x, y) = 1023 y} , where x=units of labor y=units of capital The marginal productivity of labor is evaluated as, (:se - esem | 2011 | 32.1024 32,1024 = 64 Therefore, the marginal productivity of labor is f(x,y) 132.1024 = 1641. The marginal productivity of capital is evaluated as, 6,65%) = 1:1 (0 -|(32.1024) 32.1024) Therefore, the marginal productivity of capital is f, (x,y) = 4. b) From part (a), it is clear that a unit increase in labor results much faster increase in productivity than a unit increase in capital. Therefore, Should the government encourage capital investment rather the increased expenditure on labor at this time in order to increase the country's productivity? Yes O No