Determination: Price Interaction of Supply and Demand
Economics is the only field in which two people can share a Nobel Prize for saying opposing things
Price Determination: Interaction of Supply and Demand
Objectives:
1. 2. 3. 4. 5. 6. Examine interaction of supply and demand forces in determining market price Describe concept of market structure Illustrate price determination under perfect comp Discuss length of run in agricultural price determination Firm-level economics of perfect and imperfect comp Discuss price discrimination
Market structure
State of a market with respect to competition. Market structure depends on such characteristics as:
number of buyers and sellers (economists commonly assume many buyers and then differentiate mkts by the number of sellers) their size distribution degree of product differentiation ease of entry into market
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Markets can be classified as:
Perfect competition - many sellers of homogenous product (a number of agricultural products) Monopolistic competition - many sellers of similar, but differentiated product (magazines) Oligopoly a few large firms selling
Less competition
homogeneous products (pure oligopoly), e.g., aluminum differentiated products (differentiated oligopoly), e.g., breakfast cereal Monopoly - one seller of unique product
How would you classify following markets?
U.S. corn farmers New car market in Ithaca Higher education market Electric utilities
Perfectly competitive market has following traits:
1. Large number of sellers (price takers) each is so small in relation to the entire market that no buyer or seller can affect the products price Homogenous product the product of each seller is identical to that of others No barriers to entry all resources are completely mobile; it is costless for resources to enter or leave the market Perfect information on prices and costs all buyers and sellers have perfect knowledge of the relevant forces determining prices No artificial restrictions on demand, supply, or prices
2.
3.
4.
5.
Some industries satisfy most of the above assumptions. Eg. In NYSE, many people buy and sell shares of stocks of IBM. However, no market is perfectly competitive, some markets approximate competitive conditions, and are defined as purely competitive.
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barriers to entry
Source: Perloff 1994, Modern Industrial Organization
Barriers to entry can include: advertising, customer loyalty, patents, and government regulations, etc.
Price determination under perfect competition
Sellers objective: get highest price Buyers objective: get lowest price Collective interaction => equilibrium price Equilibrium price determined where quantity supplied equals quantity demanded
Market equilibrium
Price Supply
P*
Demand Q* Quantity
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Equilibrium price is only stable price
Price P excess supply (surplus) Supply
Demand Quantity Qd Qs Suppliers are unable to sell all they want at the going price; therefore, they respond to the surplus by cutting their prices. P continues to fall until the mkt reaches the equilibrium.
Why?
Governmental policy can create surplus: minimum wage law
Wage W $3/h excess supply (surplus) Labor Supply
Labor Demand Qd Qs Quantity
Impact of the minimum wage law: surplus of labor, i.e., unemployment Q: what if the minimum wage is below the initial equilibrium?
Equilibrium price is only stable price
Price Supply
P Demand
Qs Qd
Quantity
Why?
excess demand (shortage) Demanders are unable to buy all they want at the going price; therefore, with too many buyers chasing too few goods, sellers can respond to the shortage by raising their P without losing sales. P continues to rise until the mkt reaches the equilibrium.
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Numeric examples
Assume following market demand and supply functions for compact disks
Qdcd = 0.1 - 1.2 Pcd + 0.7 Ptape + 0.4 Inc + 0.2 Tastes Qscd = 33 + 0.9 Pcd - 0.9 Plab - 0.4 Penerg + 0.4 T
Variable Pcd Ptape Inc Tastes Plab Penerg T Definition Price of CDs Price of tapes Income Consumer tastes Price of labor Price of energy Technology Mean 9 30 10 30 10 5 Unit $ $ $1,000 unit $ $ unit
Algebraic examples (contd)
Step 1: Transform demand equation in form: Qdcd = Intercept - 1.2 Pcd
Variable Ptape Inc Tastes Net effect Mean 9 30 10 * Coefficient 0.7 0.4 0.2 = Effect 6.3 12 2 20.3
Net effect of demand shifters on demand is 20.3, which is added to intercept term: Qdcd = 0.1 - 1.2 Pcd + 20.3 = 20.4 - 1.2 Pcd
Algebraic examples (contd)
Step 2: Transform supply equation in form: Qscd = Intercept + 0.9 Pcd
Variable Plab Penerg T Net effect Mean 30 10 5 * Coefficient -0.9 -0.4 0.4 = Effect -27 -4 2 -29
Net effect of supply shifters on supply is -29, which is added to intercept term: Qscd = 33 + 0.9 Pcd - 29 = 4 + 0.9 Pcd
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Algebraic examples (contd)
Step 3: To solve for equilibrium price, equate Qscd = Qdcd and solve for Pcd: 20.4 - 1.2 Pcd = 4 + 0.9 Pcd 16.4= 2.1 Pcd Pcd* = 7.81 To get Qcd*, plug Pcd* = 7.81 into either Qscd or Qdcd Qscd = 4+ 0.9(7.81) = 11.03 = Qcd*
Algebraic examples (contd)
Alternatively, construct demand and supply schedules: Qdcd 20.4 14.4 8.4 2.4 -3.6 Pcd 0 5 10 15 20 Qscd 4 8.5 13 17.5 22 Pcd 0 5 10 15 20
Qdcd>Qscd Qdcd<Qscd
Pcd Qscd = 4 + 0.9 Pcd
7.81
Qdcd = 20.4 - 1.2 Pcd 0 11.03 Qcd
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Example 2: Suppose S and D for paper in price inverse form are:
Ps = 4 Qs (supply in price inverse form) Pd = 12 - 2 Qd (demand in price inverse form) Ps = Pd = P* (equilibrium condition) Solve for P* and Q* by equating and solving for Q* 4 Q = 12 - 2 Q 6 Q = 12 Q* = 2 P* = 8
Tax/subsidy on sellers or buyers
First express all S and D functions in price inverse form P A. Tax on sellers:
Supply curve shifts left (up) by the tax
B. Subsidy on sellers:
Supply curve shifts right (down) by the subsidy
Tax on Seller
C. Tax on buyers:
Demand curve shifts left (down) by the tax
D Q
D. Subsidy on buyers:
Demand curve shifts right (up) by the subsidy Tax (t) On seller A: Ps + t is the new S fnc On buyer C: Pd t is the new D fnc Subsidy (r) B: Ps r is the new S fnc D: Pd + r is the new D fnc
Tax on buyer
P
D Q
Ps = 4 Qs Q* = 2 Pd = 12 - 2 Qd P* = 8
1.
Tax on sellers and equilibrium change
2.
3.
$6 per unit tax (t) on seller: supply curve shifts up by t supply becomes (by adding tax to the inverse supply function): Ps = 4 Qs + 6 Ps=4Qs+6 New equilibrium with tax: 4 Q + 6 = 12 - 2 Q, solve for Q P Ps=4Qs Q* = 1 (only one equi quantity) Ps* = Pd* = 4*1+6 = 12-2*1= 10 Pd* = Ps* Buyers pay a price of $10/unit to sellers For the $10/unit that sellers receive, Tax Net Ps* $6 goes into govt $4 left for sellers D Pd* = Net Ps* +t Q Pd* = 10 (buyers price) Net Ps* = 10 - 6 = 4 (sellers net price) Even though the tax is levied on sellers, buyers and sellers share the burden of the tax: buyers pay $2 extra for each unit, sellers receive $4 less for each unit
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Ps = 4 Qs Q* = 2 Pd = 12 - 2 Qd P* = 8
1.
Tax on buyers and equilibrium change
2.
3.
$6 per unit tax on buyer: demand curves shifts down by t demand becomes (by subtracting tax from the inverse demand function): Pd = 12 2 Qd - 6 = 6 - 2 Qd New equilibrium with tax: 4Q=6-2Q P Q* = 1 (only one equi quantity) S Ps* = Pd* = 4*1 = 6-2*1= 4 Net Pd* Sellers receive a price of $4/unit from buyers For buyers, on each unit Tax Pd*=Ps* pay $4 to sellers Pd=12-2Q need to pay $6 to govt Net Pd* = Ps* +t Pd=6-2Q Q Ps* = 4 (sellers price) Net Pd* = 4 + 6 = 10 (buyers net price) Even though the tax is levied on buyers, buyers and sellers share the burden of the tax: buyers pay $2 extra for each unit, sellers receive $4 less for each unit
Subsidy
The S and D for corn is the following: Ps = 5 Q Pd = 10 - 5 Q a. Solve for Q* and P* b. To encourage production, govt gives farmers a subsidy of $5 per unit produced. What is the new Q* and P*?
The effect of taxessummary
Taxes discourage market activity. The quantity of the good sold is smaller in the new equilibrium. Taxes on buyers and taxes on sellers are equivalent. Tax places a wedge between the price that buyers pay and the price that sellers receive. In the new equilibrium buyers pay more and sellers receive less for the good. Q1: Why are taxes generally considered inefficient? A: Where there are no externalities, this is case because taxes lead to output reductions. In case of externalities, taxes may be efficient since they lead to output reductions Q2: What determines incidence of tax between consumers and producers? (tax incidence: the study of who bears the burden of taxation) A: Magnitude of own price elasticity of demand relative to supply Q3: Under what condition do consumers pay more of the tax? A: A tax burdens falls more heavily on the side of the market that is less elastic. Therefore, if |own price elasticity of demand| < own price elasticity supply, consumers pay more of the tax. (there was a typo in the original note, please correct that)
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A tax burdens falls more heavily on the side of the market that is less elastic
Supply Price Price Demand Supply
P* Demand Q* Quantity
P*
Q*
Quantity
|own price elasticity of demand| > own price elasticity supply
|own price elasticity of demand| < own price elasticity supply
Length of run in agricultural price determination
Production lags for many ag goods => output predetermined by past decision Very short run - supply of nonstorable good is perfectly inelastic. Supply vertical line, implying supply consists only of the current seasons production. Given fixed supply Q1, price is determined from the inverse demand function P = D-1(Q1)
Price P3 P1 P2 D Q3 Q1 Q2 Quantity S3 S1 S2
Storable commodities in very short run (ignore imports)
Supply = production + inventories inventories = beginning inventory ending inventory
+ for inventory decrease and - for inventory increase
Price PD P* D A B Quantity Production
Case 1. High production, low market price Store AB as new inventories ( inventories < 0 in this case)
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Storable commodities in very short run
Price P* PD D C D Quantity Production
Case 2. Low production, high market price Add CD to market from inventories ( inventories > 0 in this case)
Result: storage makes effective supply more elastic than previous cases in very short run
Price current production S w/storage = production plus inventories
inventories <0 add to inventory inventories >0 release inventory 0 A B Inventory depleted
Quantity
Allowing for storage also reduces price variability
Short run and long run
Short run: a sufficient length of time for producers to respond to price changes; supply function has a positive slope S and D usually price inelastic in agriculture Long run - S and D of ag commodities more elastic P P* P* D Q* Q Q* D Q Short run price determination S P Long run price determination S
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Price volatility
The magnitude of the equilibrium price change (price volatility) depends on: A. price elasticities of S and D, i.e., EDp and ESp B. direction and size of shifts in S and D Shifts in S and D cause greater price fluctuations if S and/or D is inelastic rather than elastic Price volatility in the order of largest to smallest: very short run, short run, long run
Inelastic S P S P* P* P S elastic S
D Q Q* A. price elasticities of S and D
D Q*
Q
Price volatility - continued
P S P* P* P S P* P S
D Q*
Q Q*
D
Q Q*
D
Q
B. direction and size of shifts S in and D S and D will shift over time, hence so will P* and Q* if shifts in D and S are equal and in the same direction, P* remains constant if S increases relative to D, P* falls if D increases relative to S, P* increases
Firm-level analysis of types of competition
Analysis so far based on perfectly competitive (PC) markets While ag mkts come the closest to PC, there are deviations cooperatives increased concentration in food tendency in food manufacturers, grain exporters, and other buyers of commodities milk marketing orders fruit and vegetable marketing orders
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Market structures (in food and fiber)
1. Perfect competition: e.g., grain farmers Characteristics: many farmers selling standardized product farmers unable to influence price price represents demand farmers face
P
Firm
P
Market
D=P=MR
D Q
Firm and market demand curves under perfect competition individual firm can sell any proportion of the firms output at the then prevailing price without influencing it nonetheless, the collective actions of individual firms aggregate into market demand that determines market price (with market supply)
Q
Price
MC AC
Price
MC AC
P1
D=P=MR
P1 D=P=MR
Quantity Quantity q1 Long run q1 Farmer max profit by producing q1, where MR=MC. Why? Rational people think at the margin Suppose MR > MC, then . Suppose MR < MC, then . In short run, excess profit > or < 0 In long run, firms that remain in the market must be making zero economic profits at the end of this process of entry and exit In essence, because the firms MC curve determines the quantity of the good the firm is willing to supply at any price, it is the competitive firms supply curve
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Market structures (contd)
2. Monopoly: marketing orders Monopoly - single firm selling unique product which exists due to barriers to entry economic barriers. Develop a new product that has no close substitute, or the firm may operate in a market whose size permits only one firm to operate profitably legal barriers. Marketing orders allow farmers to join together and act like monopolist Distinguishing feature: demand schedule faced by the monopolistic firm coincides with the industry demand schedule; (firms demand curve same as negative sloped industry demand) Prof maximization: solution: MR = MC, where MR = P(1 + 1/EDp) Price does not equal marginal revenue. P > MR, why?
Price MC P2 excess profit AC c MR D
Quantity q2 Prof max solution is q2 where MR=MC monopolist selects the volume of output (q2), it then uses the demand curve to find the price that will induce consumers to buy that quantity (P2) Find the monopolists profit in the diagram The equilibrium price will change in response to: demand shift and cost curve change factors that shift demand or change costs result in a price change Same in long run because of barriers to entry
At the market level
P MC Pm Pc
MR
D
Qm
Qc
Q
Social cost of monopoly power Qm < Qc, Pm > Pc
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P MC Pm AA Pc B B
MR
D
Qm
Qc
Q
Loss in consumer surplus moving from PC to Monopoly = A+B CS: area below the demand curve but above market price
P MC Pm A Pc C
MR
D
Qm
Qc
Q
Gain in producer surplus moving from PC to Monopoly = A-C PS: area above the supply curve but below the market price
P MC Pm B Pc C
MR
D
Qm
Qc
Q
Gain in producer surplus minus loss in consumer surplus from PC to Monopoly = B+C = Deadweight loss
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Market structures (contd)
3. Monopolistic comp: e.g., livestock feed mkt. Characteristics: essentially a competitive market structure but with product differentiation many sellers product differentiation: many variants of a product exist that are close but imperfect substitutes costs of entry and exit are small feed physically different among sellers successful firms receive higher prices
Product differentiation allows small firm to operate like monopolist Because product is unique, firms demand curve has a negative slope Firm follows a monopolists rule for prof max: MR = MC, and then uses the demand curve to find the corresponding price MR = P(1 + 1/EDp) In the short run, the two types of market structure, monopolistic competition and monopoly, are similar
Price MC P3 excess profit AC c MR q3 D Quantity
Profit max output is q3, where MC = MR Price is P3, and excess profit = (P3 - c)q3 > 0 in this short run solution Identical short-run situation for monopoly
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Price
MC AC P4=c D MR q4 Quantity
At this long-run equilibrium, excess profit = 0 P > MC P = AC In comparison, P = MC = AC in PC in the long run
To summarize:
Perfect Comp
Short run price Long run price Short run quantity Long run quantity Lowest Lowest Highest Highest
Monop Comp
Same as monop >PC, <Monop Same as monop <PC, >Monop
Monopoly
Highest Highest Lowest Lowest
barriers to entry
Source: Perloff 1994, Modern Industrial Organization
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Price Determination under Oligopoly
A few large producers (tennis balls, oil) Distinguishing feature: recognized interdependence among firms - Need to consider each others operations (price or quantity decision) - Firms face similar demand likely have similar cost structures - Illegal to set prices together in the U.S. => Many possible models of oligopoly pricing exist, difficult to make generalizations about price behavior.
Examples:
1. The Cournot model 2. The Stackelberg model 3. The Bertrand model
Cournot model: each firm chooses its output while believing that the output-level of its rivals remains constant; MR = MC Example: P = 10 - Q, and Q = q1 + q2, MC1= $5, MC2 = $3 1. 2. 3. 4. 5. 6. TR1 = [10 (q1 + q2)] *q1 = 10 q1 q12 - q1q2 MR1 = 10 - 2q1 - q2 MR2 = ? MR1 = MC1 MR2 = MC2 Cournot equilibrium P, q1, and, q2? Equilibrium profits?
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Stackelberg model Firm 1 set its output first, and then Firm 2 after observing Firm 1s output, makes its output decision; Firm 1 must therefore consider how firm 2 will react
Bertrand model: firms set prices rather than output. Each firm chooses (competes) the price at the same time. If consumers have complete information and realize firms produce identical products, they buy the one with lowest P - if P1 > P2 => Q1 = 0 and Q2 =Q - if P1 < P2 => Q1= Q and Q2 = 0 - if P1 = P2 => Q1= Q2 = 0.5Q - by a slight price cut, a firm captures all its rivals business Eventually, P = MC, firms make zero profits and no firms can increase its profits by raising or lowering its price
Price discrimination (PD)
Monop may further increase revenue by PD if two conditions hold: 1. Possible to identify 2 or more groups of buyers with different price elasticities of demand 2. Market can be separated to prevent arbitrage If 1 and 2 exist, revenue increased by charging higher price in more inelastic market; and lower price in more elastic market (annual member fee at Cornell golf for student? For faculty?) PD may be prohibited by law (under Robinson-Patman Act, 1936) But, ag price discrimination from marketing orders or coops for a few farm commodities is permitted exempt
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Membership
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Two ways to PD, A: Income 1. Possible to identify 2 or more groups of buyers with different price elasticities of demand 2. Market can be separated to prevent arbitrage B: Time
Illustration of increased revenue due to PD
Assume 2 groups of buyers with differing EDp Prof max rule: allocate quantities between mkts up to point where MRmkt1=MRmkt2
Why? Because ...
PD requires different demand elasticities => different demand => different MR curves Charging same price => MRs different
With same P, MR1 < MR2
Price P Mkt 1 less elastic Price P MR2 MR1 MR1 q1 D1 Quantity q2 MR2 D2 Quantity Mkt 2 more elastic
Common price P, q1 in mkt 1 and q2 in mkt 2 Given q1 and q2, MR1 < MR2 Why is this not optimal? Because transferring part of the available supply from the mkt with the lower MR to the mkt with higher MR increases total revenue.
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Equal MRs, different prices
Price P1 P2 MR1 = MR2 Mkt 1 less elastic Price Mkt 2 more elastic
MR1 q1
D1 Quantity q2
MR2
D2 Quantity
P P1
less elastic mkt 1
P
more elastic mkt 2
P
mkt 1 + mkt 2 MC
P2 D1+D2 MR1+MR2 MR1 q1 D Q q2 MR2 D Q q1+q2 Q
Optimum total output under PD and profit-maximizing allocation of total output between mkts
Example of Legal Price Discrimination Milk Marketing Orders
Authorized by federal legislation in 1930s Allows dairy farmers to price milk according to use of the raw product => milk going into fluid products gets highest price-Class I => milk going into soft products gets Class II price => milk going into cheese gets Class III price milk going into butter-nonfat dry milk gets Class IV price Q: Which class of milk is more price inelastic?
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Class use Class I - fluid milk Class II - e.g., frozen dairy Class III - e.g., cheese Class IV - e.g., butter
Price elasticity -0.285 (Brandow) -0.550 (Brandow) -0.700 (Brandow) -0.850 (Brandow)
Two-Product Example - Milk and Manf Products Under milk marketing orders: Processors of milk pay Class prices Farmers received blend prices Example: Processor 1 2 3 Total Class I 500 0 500 1,000 Class II 0 500 500 1,000 Total 500 500 1000 2000
Suppose Class I price = 15 Class II price = 10 Revenues Processor 1 2 3 Total
Class I 7,500 0 7,500 15,000
Class II 0 5,000 5,000 10,000
Total 7,500 5,000 12,500 25,000
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Market-wide utilization of milk is 50% Class I 50% Class II => Blend price = 0.5x$15 + 0.5x$10 = $12.50, or Blend price = total revenue/total quantity = 25,000/2000 = $12.50
Two-Product Example - Illustration
Price Pf S PM Dm S: milk supply Df: fluid milk demand Dm: manf milk products demand In principle both class prices are subject to regulatory control, discretion actually exists only for fluid milk prices. Pf can be set administratively PM is national price determined by natl S&D for manf milk products. Without PD regulation: Pf = PM Equilibrium quantity: ? Total Revenue:?
Df Qf Q* Qmilk
Two-Product Example with PD
Price Pf PB PM A
Quantity sold from A to B receives this price
Pf is set administratively at high Milk producers respond to the bled price Combined demand schedule is now AB With PD regulation: Equilibrium quantity: ? Total Revenue:? Results: Pf > PM Farmers receive PB Larger total revenue
B
S Dm
Df Qf Q* Qmilk
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Source: Mankiw
Discussion questions
What are the four characteristics that determine market structure? What does a firms demand curve for perfect competition look like? Is it possible to have excess profit for perfect competition in the short run? What about the long run? Is it possible to have excess profit for monopolistic competition in the short run? What about in the long run?
Discussion questions (contd)
What are the differences in price and quantity between perfect competition and monopoly? What are the two conditions for successful price discrimination?
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