Assume that the aggregate production is given by the following: Y = K”(AN)3L1′”‘3 Y stands for output, K stands for the capital stock, N stands for…

please demonstrate this analytically for diminishing marginal returns

Assume that the aggregate production is given by the following:Y = K“(AN)3L1’“’3 Y stands for output, K stands for the capital stock, N stands for the number of the peopleemployed, L stands for the quantity of land used in production, and A stands for a measure of labour efficiency. a: and ,3 are parameters whose values are between t} and 1. a) Derive an analytical expression for the marginal product of capital (II/113K), marginalproduct of labour (MI’N), and marginal product of land (MPL) Show analytically thatthe MPK, MPN and WL exhibit diminishing marginal returns by examining thesecond derivative of the production function. 1h) Assume that a: = fl = E; K =125, L = 64 andA = 8. Find the expression for thelabour demand (Nd). Now assume that the labour supply is given by the following: NIH N 5 = H:where w is the real wage rate. 1:} What are the equilibrium levels of the real wage rate, employment and the total output (1’)- d) Suppose labour efficiency declines to A = 1, what happens to the equilibrium levels ofthe real wage rate, employment and the total output (Y) compared to part (c).

 
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