Profits, Shutdown, Long Run and FC © 1998,2010 by Peter Berck

Profits We know that a firm maximizes its profits when p = mc or when q = 0. But which? Profits are Revenues less Costs – Profits are PQ – C(Q) – = Q { P – AC(Q) }

P - AC(q*) AC AVC MC Q $/unit P q* AC(q*) P - AC(q*)

Profit Box AC AVC MC Q $/unit P q* AC(q*) P - AC(q*) Box is P - AC(q*) high and q* wide q* {P - AC(q*) = Pq* - C(q*) = 

Categorizing Cost VC are costs exclusive of fixed capital FC is the financial obligation to pay for fixed capital

Shutdown Let q* given by mc(q*) = p be quantity that maximizes profit among those quantities that are nonzero. if q = 0, shutdown, profit is -FC if pq* - vc(q*) < 0 then profit is – {pq* - vc(q*)} - FC < -FC – firm maximizes profits by setting q = o – called shutdown

Shutdown Point pq* - vc(q*) = q* (p - avc(q*) ) – so shutdown if p - avc(q*) <0 – but the minimum point of the U shaped avc curve comes where mc(q) = avc(q), so – the least price at which the firm operates is the minimum point of avc.

Shutdown Point, P s AC AVC MC Q $/unit PsPs q* At P s  = {P s - AC(q*)} q*. By construction, P s =AVC(q*) so  = {AVC(q*) - AC(q*)} q* and by definition of AFC  = {-AFC(q*)} q* = -FC. For any lower price, profit is less so P s gives minimum point at which production is not zero.

Firm’s Supply Curve A firm’s supply curve is its marginal cost curve above average variable cost

Are all costs Present and Accounted for? Suppose firm uses clean air as part of production process and doesn’t pay for it??? suppose value of clean air used is t per unit of output. (value of lost breathing!) t is the external cost of making the output mc are the private or internal costs of making output where external (jargon: externality) means external to the firm

Case for regulation firm sets p = mc – doesn’t account for t cause doesn’t pay t social cost is private + external = mc +t – correct answer is mc + t = p Charging a tax of t, the costs borne by society and not paid by firm, “internalizes the externality” (yuck) and makes the firm pay all the costs of its operation

The picture D q p mc mc + t What happens to quantity of polluting output? Price to consumers, to firm? Tax revenue? Firms’ profits? q1q2 p1 pcpc p firm

Long Run Each firm with U-shaped cost curves has a particular fixed capital stock In short run, capital stock is fixed and so is number of firms Long run, number of firms (hence capital) varies.

Entry and Exit If profits are positive, firms enter If profits are negative firms exit – Each firm is the same as the other firms – Each firm has U shaped cost curves We define Long run supply and Long Run Competitive Equilibrium

Supply from 4 Firms AC AVC MC Q $/unit S4S4 Supply from N identical firms is S N (p) = N S(p) where S is the supply curve for a single firm.

Short run supply AC AVC MC Q $/unit S4S4 when there are 2, 3 or 4 firms S2S2 S3S3

Short Run Equilibrium Three firms, so supply is S 3 D = S 3 determines price, P Output per firm is q*, total output 3 q* Profits per firm are green box AC MC Q $/unit S3S3 P D q* 3q*

Positive Profit means Entry Firm enters; New supply S 4 S 4 = D at new lower price, p’ Profits = 0 AC MC Q $/unit S4S4 S3S3 p’ q’

Long Run Supply Since firms enter at prices above p’ and leave at prices below, p’ is the price in the long run and by adjusting number of firms any amount of output will be made at this price. Q= any and p = p’ is the long run supply curve MC Q $/unit S4S4 S3S3 p’ q’

Long Run Competitive Equilibrium P = MC(q’) for each firm (and p’ > AVC min ) P = D(N q’) Profits = 0 MC Q $/unit S4S4 S3S3 p’ q’

Who pays for pollution in the long run model? Recall: C(Q with a tax) > C(Q with TBES) >C(Q) – Tax and TBES are set to use same technique, but with tax have to pay for remaining pollution So AC(Q with a tax) > AC(Q with TBES) >AC(Q)

Who pays? Which is more effective Q $/unit p’ q’ tax tbes