Question

Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started looking at the cost function C (x), the cost of a firm producing 2 items. An important microeconomics concept is the marginal cost defined in (non-mathematical introductory) economics as the cost of producing one additional item. If the current production level is o items with cost C(2), then the cost of computing h additionial items is C (x +h). The average cost of those h items is (C(x+h)-C(x)) As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h→0, i.e. the h derivative C (2). Use this function in the model below for the Marginal Cost function MC (2). Problem Set question: The cost, in dollars, of producing 2 units of a certain item is given by C(x) = 0.03.23 – 5x + 350. (a) Find the marginal cost function. MC (2) = (b) Find the marginal cost when 40 units of the item are produced. The marginal cost when 40 units are produced is $ (c) Find the actual cost of increasing production from 40 units to 41 units. The actual cost of increasing production from 40 units to 41 units is $

Answer 1

Given a Cla)=0.03-5% +350 lim cath) -((a) _ c'(a)= ho b (4+k)? 0.03(x+h) 3- 5(x+1) +350 = 0.03( 34 3+h3+33%h+3863) -51-5h+350 = 0.037*+0.03h3+0.098%b +0.093162 -58-5ht 350. 3 .: Cloth) - ((x) = 0.034 370.03h3+0.092 h +0:093h2-54-sh +350 - (0.0333-54 +350) ooohu -0.03h3+0.09x?ht 0.09362-58-5h +356-01B x3 0.03h3+0.09%+0.0982-sh n [0.03h +0.09 .0936-5] lim Cloth) – CC) + 581 –350 +000 h , h-o h die K [0.03h2 +0.0922+0.09 xh - 5 ń - hao

2 lim (0.03h? +0:09 ho +0.0931-5) = 0.03(0)+0.89372 +0.09860)-5 = 0+000911²+005 = 0.0982_5 ic'(= 0.0922-5. .: MC(n)=0.09812-5 ے McCuo) = 0.09(40)-5 =0.09x1600-5 = 144 - 5 = 139 MC(40) = 139 C(41) -C(40) (0.0914112-5)-(0.09(40)*-5) ul-yo 0.09 (1681) - $ - 144 + 151.29-144 $7:29 The actual cost of production from noto ul units $7.29 c