Consider a perfectly competitive market in which there are 100 firms (producers) and 50 consumers (buyers).

Each of the 100 firms has an identical total cost function ofTC(q)=100+4q+5q2.Each firm's marginal cost is thereforeMC(q)=4+10q.

Each of the 50 consumers has the identical demand curve given byq=1-0.1P.

(a) If the market price in this market is $6, how many units will each individual firm produce?If the market price is $3.50, how many units?(CAREFUL!Make sure they don't want to shut down.)In general, for any market priceP, write down the "supply function" that describes how many units each individual firm will produce at that price.

There are 100 identical firms in this market.What, therefore, is the overall market supply curve?(I.e., for any market priceP, what is the total quantity that will be supplied in this market?)

(b)What is the market demand curve in this market?(I.e., for any market priceP, what is the total quantity that will be demanded in this market?)

(c) What is the market equilibrium price and quantity?

(d) Suppose 20 consumers leave the market.What is the new equilibrium price and quantity?

(e) Ignore part (d).Suppose 100 firms enter the market.What is the new equilibrium price and quantity?(Continue to assume that all firms are identical.)

(f) Ignore parts (d) and (e).Suppose that production costs change such that it now costs $0.50 more to produce each unit than it did before.What is the new equilibrium price and quantity?

(g) Ignore parts (d), (e), and (f).In the long-run, describe qualitatively what will happen in this market.I.e., relative to the short run equilibrium you calculated in part (c), will the number of firms increase or decrease?Will the price increases or decease?The market quantity?(If you want to calculate the quantitative answers here, that's fine, but not required.)