Question

1.1. What is the set of profit-maximizing inputs if the profit function of a firm is given by:

π(X, Y) = P ln[X + aY] – wX – wY

where

P - price of output

f(X,Y) = ln[X + 0.5Y] - production function

X - input 1, X>=0

Y - input 2, Y>=0

w - same price of input for inputs 1 and 2

a - parameter between 0 and 1

1.2 What is the set of profit-maximizing inputs if the profit function of a firm is given by:

π(X, Y) = 20 ln[X + .5Y] – 2X – 2Y

X - input 1, X>=0

Y - input 2, Y>=0

Answer 1

dx Xt0.5Y dT - 05 on Xto.5Y o euion a) Profou)- from eq ation (lj ge me те

1.Q. )equation fiom eqation (a) Y-10 profit-inl5]-ab= 1.609-ao= -18.3 JFO from equation( x-10 do fo cured by emply ng y