Question

Given the following cost function, determine the underlying production function.

1 2

C(mi, w, y) = 10w wy, where y is the output and w and w, are the prices of two inputs

x and x, respectively.

Answer 1

Given:

$C(m,w,y)=10mwy$ as the cost function

where;

y=output

m=price of product x₁

w=price of product x₂

production function is calculated as,

$10mwy+P=mx_1+mx_2$,

where p represents profit and 10mwy is the cost function

$y=\frac{mx_1+mx_2-P}{10mw}.......................................production\space function$