0? b) For what values of w will the optimal x be zero? c) For what values of w will the optimal x be 10? d) What is the factor demand function? e) What is the profit function? f) What is the derivative of the profit function with respect to w?

July 27, 2021/in Samples /by Frank Main

The production function of a firm is given as

f(x)=20x-x2

The price of output is equal to 1. Let w be the price of the
x-input. We must have x > 0.

a) What is the first-order condition for profit maximization if x >
0?

b) For what values of w will the optimal x be zero?

c) For what values of w will the optimal x be 10?

d) What is the factor demand function?

e) What is the profit function?

f) What is the derivative of the profit function with respect to w?