Question

This is the only information I was given in the question.
N(x,y) = 10(x^0.8)(y^0.2) where x is the number of units of labor and y is the number of units of capital required to produce N units of the product. What is the marginal productivity of labor and the marginal productivity of capital? What are they when there are 40 units of labor and 50 units of capital? Nx(x,y) = 8y^.2/x^.2 Nx(40, 50) = 8.365 Ny(x,y) = 2x^.8/y^.8 Ny(40, 50) = 1.673 If each unit of labor costs $100, each unit of capital costs $50, and $10,000 is budgeted for production of this product, what is the constraint equation? What is F(x, y, 2)? Use h instead of 2. What are Fx(x, y, h), Fy(x,y,h), and Fn(x,y,h)? g(x,y)= F(x,y,h) = Fx(x,y,h) = Fy(x,y,h)= Fh(x,y,h) =

Answer 1

are Solution fou given Problews:- We that, giren 0.3 70.2 the multi-variable function N(41Y) = 102 we need to Nx, Ny Na = 2 ON = 10 yºr?[0.970.8-1) = ?($)' Ny = 3 = 10 x*-2 (0.2 yol-l] . 2 ) and 0.2 Now, N4(40,50)= 91 20030.2-1!) and Ng (40,50) = 2(190008 7243) and Constraint equition is given by 1001+ 50y = 10,000 2n+ y = 200 Now, giny)- 2x+y -200=0 Flaly, W) = n(114)-hf (any) fx = 9 h = 20 m ho m = 8 ( 24 ) 0:2 h Similarly, fy 2030.4-zh fn = Anty - 200 Now, the criticel points How .f (nuy,h) Olluns at fx=0, fy=0, x=0 *(*): A ; 1)^^ - A , 21+y = 200 1600 and h= (3)08 * 16yty=200, y = 200 and a= Now, we can similarly find out the new values of niyeh when the budget is increased by 2000 -New constraint [N 1001750 y = 12000 89=2 17

or anty=hto Jay) = 2x+y -5 +020 Now, the Critical points are Y - T7 Hence solved, Think your. 570 20 f x=160