Question

Consider a competitive industry with a large number of firms, all of which have identical cost functions cly) = y2 + 1 fory>O and c(0) = 0. (In the following problem, the output of a firm does not have to be an integer number, but the number of firms does have to be an integer.) (a) What is the firm's marginal cost? MCly) = [ans]y (b) What is the supply curve of an individual firm? S(p) = p/ If there are n firms in the industry, the industry supply curve will be Y=( (c) At what price will firms make exactly zero profits (ie the break-even price)?p* = (Hint: Take a guess at what the break-even price will be and see if it works.) (d) What quantity will each individual firm supply at this break-even price? S(p*) = (e) Suppose that the demand curve for this industry is given by D(p) = 42 - p. At the firms' break-even price p*, what will be the quantity demanded? D(p*) = (f) How many firms must be in the industry in order for the total quantity supplied to equal total quantity demanded at the break-even price?

Answer 1

6 Ne= aclar TML = 24 6. P: mc is a supply for egration. - P=27 Andur: S(P) = 1/2 If there are a firms in the industry, the industry Supply curve will be any Answer: Y = (AP)/2. At P. Mca ATC trim will make exactly ofers profit. c=y²+1 | ATC = (y² +1)/y HATO [Arc = cly Set, Mo=ATC >> 21:4+ 2424-1)

a youn yo $112 ally-L, MC = ATC L MC = ATC WE Set P = MC Typ.20) 122 at Prz find make exsly deco profunds. Lo sce) = 1/2 (indinckel fim dypt). 1) 3CP) = 2/1 1500) = || Indendeal time will supply yo! at break even porce CP candurri so 1 - O D(P), 42- p put p22 D(P) = 42-2 +242) - 40 0. Y =) () 1 (np)/2 = 40 (21/2) = 40 1 (n=40 grantly demanded at p=2 is 40 Answer: DC p.) = 40 Then are 40 firms is the industry. Andwani na 40.