Profit Maximization in Competitive Markets

Firm behaviour Proﬁt Maximization

in Competitive Markets To explain firm behaviour we separated the Finding the Supply Function decision process artificially into two steps: 1 Cost Minimization: firms look for a way to produce any (given) output as cheap as possible. Herbert Stocker → optimal factor allocation! As a result we get factor demand functions and the [email protected] cost function C ∗ = C(w, r, Q). Institute of International Studies This happened in the last chapter. University of Ramkhamhaeng & 2 Profit Maximization: next firms have to decide Department of Economics what output to produce. University of Innsbruck They face technological and market restrictions.

Firm behaviour Firm behaviour

Technological restrictions are already incorporated in the cost function Market restrictions differ between market (remember that the cost function was derived by structures. Therefore, we have to examine the cost minimization under constraint of the process profit maximization for different market production function!). structures separately. However, there were no assumptions for the In this chapter we’ll focus on perfect competitive output market necessary, we just assumed that markets, in the next chapter we’ll examine factor prices are exogeneously given. imperfect competition. Market restrictions refer market conditions, that is, how output price is determined.

1 Perfect Competition Perfect Competition

Firms are price-takers! A firm cannot influence the price of its product, thus it can sell any Free Entry and Exit: amount of output at the market price. This is There is free entry and exit into and from an because . . . industry when new producers can easily enter into A large number of firms in the market. An undifferentiated product. or leave that industry. Complete information available to all market Free entry and exit ensure: participants. that the number of producers in an industry can adjust In the long run competition between firms pushes to changing market conditions, and, economic profits (measured with opportunity cost) that producers in an industry cannot artificially keep down to zero. This is because . . . other firms out. Free market entry and exit.

Proﬁt Maximization Revenue and Marginal Revenue

Remember, total revenue R = P × Q. Assumption: ≡ firms maximize economic profits! Average revenue: AR R/Q = (PQ)/Q = P; average revenue always equals the price! Economic profits are the difference between total revenue and total opportunity cost: Marginal Revenue (MR) is the additional revenue that a firm takes in from selling one π = PQ − C(Q) additional unit of output; or, the change in revenue divided by the change in Maximization under constraints: output Technological restrictions: incorporated in cost function C = C(Q); dR d(PQ) ∆R Change in Revenue Market restrictions: perfect competition ⇒ P, w and MR = = ≈ = r are given by the market (price-takers)! dQ dQ ∆Q Change in Output

2 Revenue and Marginal Revenue Perfect Competition

Under perfect competition a ﬁrm can sell any Since ﬁrms are small relative to the market managers output for the market price! Therefore . . . ‘perceive’ relevant market demand as perfectly elastic! P Marginal Revenue (MR) for a perfectly

competitive ﬁrm is a horizontal line, because it MCi representative can sell any further unit of output for the same Firm Market demand price. Therefore, for a perfectly competitive ﬁrm ACi Market- price equals marginal revenue: P is ‘perceived’ supply Market demand d(PQ) MR = = P dQ

(this is true only for perfect competition, this is not true for Q other market structures!)

Proﬁt Maximization Proﬁt Maximization

Decision problem for exogeneous P: Why gives quantity where P = MC highest max :Q π = P − C(w, r, Q) P Q MC possible profits? Lost A necessary condition for an optimum is (quantity Q is Profit When marginal cost is MRP = the only choice variable) P∗ smaller than marginal AC revenue the firm ∂π ∂C ! = P − = 0 should produce more! ∂Q ∂Q ⇒ ⇐ When marginal revenue or “price equal marginal cost” MC MR= P MC is is smaller than ∂C Q marginal cost the firm MR = P = ≡ MC should produce less! ∂Q

3 Profit Maximization Profit Maximization Profits : − P P πQ = P C MC The firm can increase C profits until revenue for = P − Q MC Q the last unit sold equals ∗ P bc P P − Q ∗ bc = ( AC) P AC cost of this last unit, P ∗ AC i.e. until marginal rev- π Profits are highest, enue is equal marginal when the firm chooses cost: the quantity Q at

bc which ∗ P = MR = MC bc Q Q ∗ Q Q MC(Q) = P

Proﬁt Maximization Proﬁt Maximization

What happens, when P < AC? A profit maximizing firm should choose the output Remember quantity where marginal cost is equal to the exogenous price: π = PQ − C(Q) C(Q) MC(Q) = P = P − Q Q − Always? = (P AC) Q No! This will not be the case when . . . When P < AC the firm would incur losses! . . . marginal cost decrease ... P < AC In this cases profits are not maximized, but losses minimized.

4 Proﬁt Maximization Supply Function of a Firm

1) When P = P : P A Q → Minimum Ef- MC AC A ﬁcient Size AVC Supply Function of a Firm 2) When P < P : A The short-run supply function (S) of a ﬁrm on a long-run → market perfect competitive market is the increasing part of the PA bc exit → A: ‘exit A point’ marginal cost curve, that lies above the minimum of the average (variable) cost curve. bc PB 3) When P < PB: B AFC stop production bc bc → QB QA Q immediately B: ‘shut-down point’

Supply Function of a Firm Short-Run Supply Curve

When the price falls below the minimum of the Short-Run Supply Curve of a Firm: average variable cost curve (PB ) the firm will stop P production immediately −→ shutdown point. Ssr AC The portion of its When the price falls only for a short time below AVC marginal cost curve the minimum of the average total cost curve, but (MC) that lies above the firm expects the price to increase again, the average variable firm will continue production, since she still can PA cost. cover at least a part of the fixed costs (price When market price

bc between PA and PB ). PB is between PA and B AFC Only when the firm expects the price will remain PB firm runs losses, permanently below the minimum of the average QB Q but can at least cover total cost curve she will decide to leave the some of the fixed market permanently −→ exit point. costs. 5 Long-Run Supply Curve Irrelevance of Fixed Costs

P Long-Run Supply Fixed costs are irrelevant in the decision how S lr AC Curve of a Firm: much to produce! AVC The marginal cost Level of fixed cost has no effect on marginal cost curve (MC) above or minimum average variable cost. the minimum point Thus no effect on optimal level of output. PA bc A of its average total However, fixed cost are included in ATC, and cost curve. therefore may indirectly influence the long-run AFC If market price is decision of a firm to exit the market. above PA firm makes Sunk cost should have no influence whatsoever for QA Q profits. any decision of a firm!

Managerial decisionmaking Market Supply

1 Managers on competitive markets have to watch Market supply equals the sum of the quantities market price and its development closely, and supplied by the individual firms in the market. 2 to organize and monitor production efficiently! The market supply function (S) for a perfect competitive market is the horizontal sum of the individual supplies (aggregate quantities). Management on perfectly competitive markets Since quantities can never be negative only Two simple rules: positive numbers may be added. for a market with N firms: 1 Shut down if AVC > P, or exit the market if ATC > P. N S = Qi for all Qi > 0 2 If AVC < P produce the quantity where MC = P. Xi=1

6 Proﬁt Maximization and Competition Example

Firm Total Market 2 Perfect competition implies free market entry and P Ci 5= 0.7 Qi 5+ 0.7 P Shortrun market supply 5 exit. Sk = i=1 Qi MCi If the market price is above the minimum of the 4 4 P average total cost curve some firms earn economic 3 3 profits (opportunity cost!), therefore new firms π ACi will enter the market. 2 2 b b This entry of new firms pushes prices in the long 1 1 term down to the minimum of the minimum of QD = 40 − 10P the average total cost curve! 0 0 0 1 2 3 4 Qi 0 10 20 30 40 S

Example Example: long-run

Firm Total market Firm Total Market 2 P Ci 5= 0.7 Qi +5 0.7 P Shortrun market supply P P Shortrun market supply 5 5 Sk = i=1 Qi Sk = i=1 Qi MCi MCi 4 4 P 4 4 P 10 Sm = i=1 Qi longrun market supply 3 Market- 3 3 3 25 ACi entries! P ACi Sl = i=1 Qi π = 0 Market- 2 π 2 2 entries! 2 P b b b b b b b

1 1 D 1 1 D Reaction of Q = 40 − 10P Reaction of Q = 40 − 10P Firm Firms 0 0 0 0 0 1 2 3 4 Qi 0 10 20 30 40 S 0 1 2 3 4 Qi 0 10 20 30 40 S

7 Proﬁt Maximization Long-run Market Supply Curve

Short-run: Firms choose output quantity Q where marginal cost equals the market price, because this gives them the highest possible profit Market entries (exits) shift the market supply curve to the right (left). MC(Q) = P In the long run firms will enter or exit the market Long-run: However, in the long run competition until market supply curve intersects the market and market entries force the market price down to demand curve at the ‘smallest possible price’, i.e. the minimum of the average cost curve where market price is equal to the minimum of average cost. MC(Q) = P = AC Therefore, markets entries and exits drive Because of free market entry and exit the long run economic profits down to zero! market supply curve is horizontal at the minimum of the average cost curve of a firm.

Long-run Market Supply Curve Long-run Market Supply

In the long run firms will enter or exit the market until profit is driven to zero, therefore the number The long-run market supply curve can still be of firms in an industry is endogenous. increasing if In the long run, price equals the minimum of it is an increasing cost industry (diseconomies of scale or decreasing returns to scale). average total cost. factors are scarce and become more expensive with The long-run market supply curve is horizontal increasing demand. (perfectly elastic) at price P = ACmin: firms are differently efficient or own unique factors. P In this case market price will reflect the minimum long-run market supply average cost of the marginal firm. The marginal firm is the firm that would exit the market if the price were any lower.

8 Short-Run Producer Surplus Short-Run Producer Surplus

Short-Run Producer Surplus: the area above the short-run supply curve that is below market price over the range of output supplied. Short-run producer surplus is the amount by which total revenue (TR) exceeds total variable cost (TVC). Short-run producer surplus exceeds economic proﬁt by the amount of total ﬁxed cost (TFC).

Attn: Short-Run Producer Surplus is based on the AVC curve, not TAC!

Economic Rent Economic Rent

Economic Rent: Payment to the owner of a scarce, superior resource in excess of the resource’s opportunity cost. In long-run competitive equilibrium firms that employ such resources earn zero economic profit. Potential economic profit is paid to the resource as economic rent. In increasing cost industries, all long-run producer surplus is paid to resource suppliers as economic rent.

9 Summery Long Run Strategies for Managers

Managers in competitive industries are in a difficult Managers on perfectly competitive markets have situation, since they can only control cost. In the long little or no control over product price. run they can try to gain market power by . . . They compete on basis of lowering costs of Differentiating products. production. Forming producer association to change consumer One way of reducing cost is finding the ‘Minimum preferences and increase demand for output of the Efficient Scale’ for the industry. entire industry. Perfectly competitive firms earn zero economic Merging with other companies. profit because entry of other firms compete away excess profit. Any Questions?