Question

Question 1: Cost Minimization and Cost Curves Suppose that Jennifer produces good y by using input xi and x2. The production function which Jennifer faces is: y = x} + x] The cost for every unit of xi is wi and the cost for every unit of x2 is w2. There is a fixed cost component F, which also forms a part of her total cost. (a) Write down the cost minimization problem. Solve this problem and express x1/x2 as a function of w2/w1.

Answer 1

1) Given Production function: Write down Cost minimization problem: Minimize : Total cost (TC)=F+w-X; +W, X3 Subject to : y = x2- Here, wy, W, > 0 and X1, X2 > 0 Total Cost (TC) is minimized when marginal rate of technical substitution (MRTS) is equal to price ratio. a = b ) :(9.). sap (). (or)

Find the conditional demand for x and x. Plugging into the production function y = x + x2 (w+w, WP (w, +w.)

Observed by above computation, with increase in y, demand for x and demand for x will increase Simply increases, and with increase in w, demand for x With increase in w, demand for increases. With decrease in w, demand for x decreases, and with decrease in wg, demand for x decreases. (c) Found the conditional demand. Find the average cost (AC), average variable cost (AVC), average fixed cost (AFC), and marginal cost (MC): Given, F = 6,44 = 2 and 13 = 4 Total cost(TC)-F+w,x: +W, X, = 6 + 2xy +4x,

Thus, Total cost(TC)=6+( 4 (:TC = AC +VC) Average variable cost( AVC Average variable cos(210)_vc_3 Average fixed cost(AFC) - 40 - Marginal cos(Ac)-(50)-(6-( * )-)