Competition and Market Equilibrium Perfect Competition Defining Characteristic

Competition and Market Equilibrium

Perfect Competition • Defining Characteristic is lack of market power – Price Takers • How do we get there? – Homogeneous output (or homogeneous enough) – Enough buyers and sellers that no one (or group thereof acting together) can effect demand or supply enough to affect market price – Perfect information (all participants know the market price) – Free entry and exit in the long run (to ensure price = MC)

Supply and Demand • The workhorse model of economics assumes perfectly competitive markets. • Seems odd since so few markets satisfy all conditions, but predictive power holds for markets that are less competitive.

Why do economists like them so much • With competitive markets, when all goods are private, there are no externalities and we don’t worry about income distribution… • Markets – Produce goods at the lowest possible cost (technical efficiency) – Commit all resources to their highest use (we produce the mix of goods people want as cheaply as possible) – Goods and services are consumed by those who value them most (maximize economic surplus, but not utility)

Technical Efficiency: Two Apple Growers of Many $ $ SMC $1. 20 SMC $1. 00 q* q • Both farmers are producing at q* to start. Total cost of production can be lowered if Farmer Blue produces one fewer apple and Farmer Red produces one more. • To minimize total cost of producing apples, the SMC of the last apple produced by every farmer must be the same. • Perfectly competitive industries get this result.

Allocative Efficiency Ratio of market price = ratio of MC Oranges Qo Qa Apples

Wow! • Any and all units of a good or service that can be produced at an opportunity cost below the value of the good to consumers will be produced (and should be produced). • What coordinates all this magic? Price. • Price – signals opportunity cost of resources to producers so they can minimize cost and know how much to produce and when to enter or exit production. – Signals to consumers the value of the resources in production so that goods and services are consumed only by those whose value exceeds cost.

This IS the Invisible Hand • Adam Smith: – Efficient Resource Allocation: Markets minimize the cost of production (only the lowest cost producers produce) – Consumer Surplus Maximization: Markets maximize the consumer surplus in consumption (highest value consumers consume) – All and only units where benefit > cost will be produced – And not only in one market for one good, but for all markets and all goods* * except for those pesky market failures

Competition vs Non-competitive Markets • While prices create technical efficiency and promote efficient rationing in less than competitive situations, allocative efficiency is lacking (monopolists underproduce) • Only in perfect competition is economic surplus maximized. • MB=MC for last unit produced, no deadweight loss.

Demand • Demand is simply the horizontal sum of individual demand curves • No short vs long run… although… • Demand becomes more elastic over time as time allows individuals to find substitutes.

Market Demand p 30 • Assume a market with 3 individuals: x 1 = 25 – 2 px x 2 = 45 – 1. 5 px x 3 = 50 – 2. 5 px • The market demand curve is the horizontal sum X = 120 – 6 px (P = 20 -. 143 X) • Except for the kinks. This equation is for this line 20 D 12. 50 25 45 50 Q

Firm and Market Supply • Very Short Run: Quantities of all inputs are fixed. • Short Run: At least one input, but not all, are fixed. • Long Run: Quantities of all inputs used are variable.

Market Adjustment in the Very Short Run When quantity is fixed in the very short run and demand increases, price will rise but quantity will not change as firms cannot increase production. P VSRS Demand for plywood increases as a hurricane approaches. D’ D Q

Market Adjustment in the Very Short Run Similarly, there can be a supply shock (e. g. hurricane) that shifts supply back P S’ S D Q

Market Adjustment in the Very Short Run P S’ S Gasoline: Price rises with supply shift. Assume an excise tax on gasoline. Politicians call for suspending the tax, but in the short run price will be unaffected as neither supply or demand would shift as a result. Tax D Q

Market Adjustment in the Very Short Run P S’ S Gasoline: Price rises with supply shift. Assume an excise tax on gasoline. Politicians call for suspending the tax, but in the short run price will be unaffected as neither supply or demand would shift as a result. Tax D Q

Short Run/Long Run Model • The more usual analysis. • Short Run – Firms produce where MR = SMC – Firms may shut down in the short run – Market supply is the horizontal sum of all firms in the industry (no entry or exit in the short run) • Long Run – Price driven to the break-even price as firms enter/exit to seek profits and avoid losses – Profits = 0 – Firm on expansion path – Capital at the level that minimizes SAC

Long and Short Run Cost Curves • Assume we start here. $ SMC MC SAC AC AVC q

Short Run • Short Run supply is SMC at P > min(AVC) – Yes, firms will produce at lower prices in SR than LR. $ SMC SAC MC AC SAVC q

Short Run Firm Supply (Algebra) SMC Above AVC

Short Run Market Supply (Algebra)

Short Run, Firm and Market • Assume we start here for short run. SMC $ $ SAC SRS SAVC PSD D q q

Long Run • Assume IRS and then DRS (no CRS) $ SMC MC SAC AC AVC q

Firm Long Run Supply • q where P = MC so long as π ≥ 0 (P> PBE) $ Firm LRS AC MC PBE q

Long Run Firm Supply (Algebra) MC above AC

Long Run Market Supply • Long run firm supply: q=4 P • So long run market supply: Q=N(4 P)? • NO!!!

Long Run Firms Enter and Exit until profit = 0 and market price = PBE • In long run: P →PBE and π → 0 $ MC AC PBE q. LR q

Long Run Market Supply • Firms enter and exit so that in the long run, LRS = the quantity demanded at the p. BE SMC P SAC MC P AC S Assumes constant cost industry, more to come on that! PBE LRS PSD D q Q

Shocks • Change in demand • Change in FC • Change in VC

Change in Demand • Short Run: price up, Δ Q is n*Δq, π > 0 SMC $ SRS 1 $ ATC AVC PBE D D q 1 q 2 q Q 1 Q 2 Q

Change in Demand • Long run: Firms enter, π > 0 SMC $ SRS 1 $ ATC SRS 2 AVC PBE D D q 1 q 2 q Q 2 Q 3 Q

Change in Demand • Long Run Supply: If the PBE does not change, the market will always supply the Qd at PBE. SMC $ $ ATC SRS 2 AVC LRS PBE D D q 1 q Q 3 Q

Comparative Statics Analysis • In the long run, the number of firms in the industry will vary from one long-run equilibrium to another • Assume that we are examining a constant-cost industry • Suppose that the initial long-run equilibrium industry output is Q 0 and the typical firm’s output is q* (where AC is minimized) • The equilibrium number of firms in the industry N 1 = Q 1/q 1*

Comparative Statics Analysis • A shift in demand that changes the equilibrium industry output to Q 3 will change the equilibrium number of firms to N 3 = Q 3/q 1* • The change in the number of firms is • In a constant cost industry q*will not change, so only the size of the shift in demand will affect the change in n.

Change in FC • Short Run: MC is unaffected, so qs is unaffected, so PM is unaffected. But firms suffer losses. SMC $ SRS 1 $ ATC AVC PBE D q 1 q Q 1 Q

Change in FC • Long run: Firms exit until the PM = the new PBE. • With higher price of K, firms use less. • Change in firm level of output is unknown. $ PBE 2 ATC’ SMC’ SRS 1 $ AVC’ PBE 1 D q 3 q Q 1 Q

Change in FC • Long run: Firms exit until the PM = the new PBE. SMC’ $ SAC’ PBE 2 SRS 1 $ AVC’ LRS 2 LRS 1 PBE 1 D q 3 q Q 3 Q 1 Q

Change in VC • Short Run: MC is affected, so qs is affected, as is PM. Firms suffer losses, as the higher price does not cover the higher cost. SMC $ SRS 1 $ ATC AVC PBE D q 1 If AVC > P, firms will shut down. q Q 1 Q

Change in VC • While firm supply decreases, qs is unknown as we don’t know the change in price. However, change in MC > change in P. SRS 2 SMC $ SRS 1 $ ATC AVC PBE D q 1 If AVC > P, firms will shut down. q Q 2 Q 1 Q

Change in VC • Again, with higher costs, and PBE, the LRS curve will shift upwards. The new q* (and optimal K) could be higher or lower. SRS 3 SMC $ PBE 2 SRS 1 $ ATC 2 AVC LRS 2 LRS 1 PBE 1 D q 3 q Q 3 Q 1 Q

Comparative Statics Analysis • The effect of a change in input prices – we need to know how much minimum average cost is affected – we need to know how an increase in long-run equilibrium price will affect quantity demanded

Comparative Statics Analysis • The optimal level of output for each firm may also be affected • Therefore, the change in the number of firms becomes • And the relative changes in Q and q* will determine the change in N.

Comparative Statics, change in q*

Supply and Demand • Basis is the competitive model – Usually, competitive market in the short run. – Sometimes used to depict competitive market in the long run with increasing cost industry assumption. • Treatment – Algebra (to get equilibrium) – Calculus (comparative statics) • Demand shifters • Supply shifters • Sales and Excise taxes

As in Intermediate Micro • Inverse Demand: P = 1, 500 -. 5 Qd • Inverse Supply: P = 600 + Qs • Solution is Q = 600, P = 1, 200 P S 1, 500 1, 200 D 600 3, 000 Q

Sales Tax, Comparative Statics • Intermediate – Add Sales Tax = $150 • • Inverse Demand: P = 1500 - tax -. 5 Qd Inverse Supply: P = 600 + Qs Solution is Q = 500, P = 1100 (consumer cost = P + t = $1250) Just by comparing outcomes, P S Market Price PD=1, 250 P*=1, 100 D Dt 500 Q

Excise Tax, Comparative Statics • Intermediate Market Price – Add Excise Tax = $150 • • Inverse Demand: P = 1500 -. 5 Qd Inverse Supply: P = 600 + tax + Qs Solution is Q = 500, P = 1250 (producer keeps = P – t = $1100) Just by comparing outcomes, P St S P*=1, 250 PS=1, 100 D 500 Q

Linear Supply and Demand, Equilibrium • General linear functions specified – Inverse Demand: P = a – b. Qd (a > 0, b > 0) – Inverse Supply: P = c + d. Qs (c > 0, d > 0) – Equilibrium condition: Qs = Qd (and Ps = Pd) • Reduced form solution (only in terms of a, b, c, d) P a slope = d S P* slope = -b D c Q* Q

Shifts in Supply or Demand, Comparative Statics • Solution P a slope = d S P* • Comparative Statics slope = -b D c Q* So long as a>c Note, “b” rising means demand must be getting steeper. Q

Sales Tax • Market Model (sales tax) – Inverse Demand: P = a - t – b. Qd (a > 0, b > 0) – Inverse Supply: P = c + d. Qs (c > 0, d > 0) – Equilibrium condition: Qs = Qd • Reduced form solution (only in terms of a, b, c, d, t) P a S a-t P D* P* Pt* D c Dt Qt* Q* Q

Sales Tax, Comparative Statics • Solution • Comparative Statics P a S a-t P D* P* Pt* D c Dt Qt* Q* Q

Supply and Demand with General Form Equations • All we assume is: • And that at equilibrium (Q*, P*): • First assume only a is changing and then only b.

Comparative Statics of a Demand Shift • Start with FD = D(P*, a) – Q* = 0 FS = S(P*) – Q* = 0 (see 8. 41 in Chiang) • Substitute in: P*=P*(a), and Q*=Q*(a) • To get FD = D(P*(a), a) – Q* (a)= 0 FS = S(P*(a)) – Q*(a) = 0 (see 8. 40 in Chiang), Implicit function theorem tells us equations P* and Q* must exist to solve these equations simultaneously. • Take the total derivative with respect to a:

Demand Shifting • From above Change in demand when a changes (Holding P constant, how does Qd change with a). Slope of demand curve so d. Qd/d. P Change in equilibrium quantity when a changes Slope of supply curve d. Qs/d. P • Matrix Notation Change in equilibrium price when a changes

Demand Shifting and Change in P* • Cramer’s Rule >0 • If a is income and the good is normal, then Da > 0 and equilibrium price will rise with a. • If a is price of a complimentary good, then Da < 0 and equilibrium price will fall with a.

Demand Shifting and Change in Q* • Cramer’s Rule >0 • If a is income and the good is normal, then Da > 0 and equilibrium quantity will rise with a. • If a is price of a complimentary good, then Da < 0 and equilibrium price will fall with a.

Supply Shifting • Start with FD = D(P*) – Q* = 0 FS = S(P*, b) – Q* = 0 (see 8. 41 in Chiang) • Substitute in: P*=P*(b), and Q*=Q*(b) • To get FD = D(P*(b)) – Q* (b)= 0 FS = S(P*(b), b) – Q*(b) = 0 (see 8. 40 in Chiang), Implicit function theorem tells us equations P* and Q* must exist to solve these equations simultaneously. • Take the total derivative with respect to b:

Supply Shifting • From above Slope of demand curve Change in equilibrium quantity when b changes so d. Qd/d. P Slope of supply curve so d. Qs/d. P • Matrix Notation Change in equilibrium price when b changes Change in supply when b changes (holding P constant, how does Qs change with a).

Supply Shifting and the Change in P* • Cramer’s Rule <0 • If b is technology, then Sb > 0 and equilibrium price will fall with b. • If b is wages, then Sb < 0 and equilibrium price will rise with b.

Supply Shifting and the Change in P* • Cramer’s Rule <0 • If b is technology, then Sb > 0 and equilibrium quantity will rise with b. • If b is wages, then Sb < 0 and equilibrium quantity will fall with b.

Results in Elasticities • We can convert our analysis to elasticities

Effect of a 1% increase in income on demand for a normal good • Assume D, M =. 5, S, p =. 75, D, p = -1. 25 . 5% increase in demand . 25% inc. in price 1% increase in income . 5% inc. in demand P . 5% S . 25% D’ D . 1875% . 25 increase in price . 1875% inc. in quantity: %ΔQs/%ΔP =. 75 %ΔQs/. 25 =. 75 %ΔQs =. 1875 Q

Effect of a 1% increase in wages • Assume S, w = -. 60, Qs, p =. 80, Qd, p = -. 70 . 6% decrease in supply . 40% inc. in price P S’ 1% increase in income for a. 6% dec. in supply . 6% S . 40% increase in price . 28% dec. in quantity: %ΔQd/%ΔP =-. 70 %ΔQd/. 40 =-. 70 %ΔQs =-. 28 D -. 28% Q

Supply and Demand (Sales Tax) • Start with FD = D(P*+t) – Q* = 0 FS = S(P*) – Q* = 0 P* is the market price, but the buyer pays PD = P*+t • Substitute in: P*=P*(t), and Q*=Q*(t) • To get FD = D(P*(t) + t) – Q*(t)= 0 FS = S(P*(t)) – Q*(t) = 0 • Take the total derivative with respect to t:

Supply and Demand (Sales Tax) • From above • Matrix Notation

Change in P* when t rises P Original Tax S D Q

Change in Q* when t rises P Original Tax S D

Supply and Demand (Excise) • Start with FD = D(P*) – Q* = 0 FS = S(P*-t) – Q* = 0 P* is the market price, but the supplier keeps Ps = P*-t • Substitute in: P*=P*(t), and Q*=Q*(t) • To get FD = D(P*(t)) – Q*(t)= 0 FS = S(P*(t) - t) – Q*(t) = 0 • Take the total derivative with respect to t:

Supply and Demand (Excise Tax) • Matrix Notation

Change in P* when t rises S P D Original Tax Q

Change in Q* when t rises S P D Original Tax Q

And Finally

Increasing Cost Industries and Decreasing Cost Industries • What happens when the market expands or contracts. – For constant cost industries, expansion and contraction of the market does not affect v and w so the break-even price remains constant. – For increasing cost industries: • Factor price effect: w, or v rise with Qe • Less efficient firm’s effect – For decreasing cost industries: • Factor price effect: w, or v fall with Qe

Short Run • Assume we start here. SMC $ $ ATC SRS AVC PBE D q Q

Increasing Cost Industry: Factor Price effect • Demand Increases SMC $ $ ATC SRS AVC PBE D’ D q Q

Increasing Cost Industry: Factor Price effect • Firms increase production in the short run SMC $ $ ATC SRS AVC PBE D’ D q Q

Increasing Cost Industry: Factor Price effect • If it is w that rises with an increased demand for labor, MC will rise with expansion. SMC $ $ ATC SRS’ SRS AVC PBE D’ D q Q

Increasing Cost Industry: Factor Price effect • Profits > 0, so firms still enter, but profit returns to zero before the price falls to its previous level. SMC $ $ ATC SRS’’ SRS AVC PBE D’ D q Q

Increasing Cost Industry: Factor Price effect • Profits > 0, so firms still enter, but profit returns to zero before the price falls to its previous level. SMC $ $ ATC SRS’’ LRS AVC PBE’ PBE D’ D q Q

SR or LR effects • Often, costs are assumed stable in SR, but increase only in the long run. • Same result, easier math.

Increasing Cost Industry: Differential Productivity Effect • Firms increase production in the short run SMC $ $ ATC SRS AVC PBE D’ D q Q

Increasing Cost Industry: Differential Productivity Effect • New firms are less efficient, so entry stops before price returns to original level SMC $ $ ATC SRS’ SRS AVC PBE D’ D q Q

Increasing Cost Industry: Differential Productivity Effect • New firms are less efficient, so entry stops before price returns to original level SMC $ $ ATC SRS’ SRS AVC LRS PBE D’ D q Q

Why differential in efficiency? • Better (lower cost) location? Rent should rise to compensate. • Better managers at some firms? Wages should rise to equilibrate costs. • Smarter entrepreneur? Should have higher opportunity cost. • More fertile land (Ricardo’s original example)

Decreasing Cost Industry • As a market expands, economies of scale in production of inputs causes input prices to fall. • As the market expands, inputs prices fall and when firms enter, the price falls below its initial level before P = PBE. • Reverse of factor price effect. • As demand for micro computers rose in the 1980 s -90 s, chip factories got bigger and prices fell (technological advances exacerbated the issue, but that is separate).

Producer Surplus • Remember the short run SMC $ $ ATC SRS AVC PBE PS=π+FC D q Q

Long Run Producer Surplus • Long Run producer surplus is long run π • Zero producer surplus if constant cost industry. SMC $ $ ATC SRS AVC LRS PBE D q Q

Producer Surplus • In an increasing cost industry, depends on the source of the upward sloping LRS curve. SMC $ $ SRS ATC AVC LRS PBE D q Q

Producer Surplus • Factor price effect, the rising price needed to increase supply of the input provides a surplus to lower cost suppliers $ $ Factor Market Output Market S LRS D D q • However, individual firms have LR π=0 and PS=0. Q

Producer Surplus • Differential Productivity Effect: if some firms have a cost advantage, the firm that owns the source will benefit in the long run. $ $ SMC ATC Output Market S LRS PBE D q Q

Long Run Producer Surplus • Farmer with the best land will earn an increasing producer surplus (long run profit). – The excess future stream of long run profits will be capitalized into the market price (value) of the land. • Actors and Athletes who are really good earn a long run profit because there is no substitute. But now we are starting to talk about market power.