The Partial Equilibrium Competitive Model

The Partial Equilibrium Competitive Model
Chapter 12 The Partial Equilibrium Competitive Model

Quantity of x demanded = x(px,py,I)
Market Demand Assume that there are only two goods (x and y) An individual’s demand for x is Quantity of x demanded = x(px,py,I) If we use i to reflect each individual in the market, then the market demand curve is To construct the market demand curve, pX is allowed to vary while py and the income of each individual are held constant If each individual’s demand for x is downward sloping, the market demand curve will also be downward sloping

Market Demand To derive the market demand curve, we sum the
quantities demanded at every price px px px x1 Individual 1’s demand curve x2 Individual 2’s demand curve Market demand curve X* X x1* + x2* = X* x1* x2* px* x x x

Shifts in the Market Demand Curve
The market demand summarizes the ceteris paribus relationship between X and px changes in px result in movements along the curve (change in quantity demanded) changes in other determinants of the demand for X cause the demand curve to shift to a new position (change in demand)

Shifts in Market Demand
Suppose that individual 1’s demand for oranges is given by x1 = 10 – 2px + 0.1I py and individual 2’s demand is x2 = 17 – px I py The market demand curve is X = x1 + x2 = 27 – 3px + 0.1I I2 + py

To graph the demand curve, we must assume values for py, I1, and I2 If py = 4, I1 = 40, and I2 = 20, the market demand curve becomes X = 27 – 3px = 36 – 3px

If py rises to 6, the market demand curve shifts outward to X = 27 – 3px = 38 – 3px note that X and Y are substitutes If I1 fell to 30 while I2 rose to 30, the market demand would shift inward to X = 27 – 3px = 35.5 – 3px note that X is a normal good for both buyers

Elasticity of Market Demand
1) The price elasticity of market demand is measured by Market demand is characterized as elastic if (eQ,P < -1) or inelastic (0> eQ,P > -1) 2) The cross-price elasticity of market demand is measured by 3) The income elasticity of market demand is measured by

Timing of the Supply Response
In the analysis of competitive pricing, the time period under consideration is important 1) Very Short Run no supply response (quantity supplied is fixed) 2) Short Run existing firms can alter their quantity supplied, but no new firms can enter the industry 3) Long Run new firms may enter an industry

1) Pricing in the Very Short Run
In the very short run (or the market period), there is no supply response to changing market conditions price acts only as a device to ration demand price will adjust to clear the market the supply curve is a vertical line

Pricing in the Very Short Run
Price S D’ P2 When quantity is fixed in the very short run, price will rise from P1 to P2 when the demand rises from D to D’ P1 D Quantity per period Q*

2) Short-Run Price Determination
The number of firms in an industry is fixed These firms are able to adjust the quantity they are producing they can do this by altering the levels of the variable inputs they employ

Perfect Competition A perfectly competitive industry is one that obeys the following assumptions: 1) there are a large number of firms, each producing the same homogeneous product 2) each firm attempts to maximize profits 3) each firm is a price taker its actions have no effect on the market price 4) information is perfect

Short-Run Market Supply
The quantity of output supplied to the entire market in the short run is the sum of the quantities supplied by each firm the amount supplied by each firm depends on price The short-run market supply curve will be upward-sloping because each firm’s short-run supply curve has a positive slope

Short-Run Market Supply Curve
To derive the market supply curve, we sum the quantities supplied at every price sA Firm A’s supply curve P P P sB Firm B’s supply curve Market supply curve Q1 S q1A + q1B = Q1 q1A q1B P1 quantity quantity Quantity

Short-Run Market Supply Function
The short-run market supply function shows total quantity supplied by each firm to a market Firms are assumed to face the same market price and the same prices for inputs

Short-Run Supply Elasticity
The short-run supply elasticity describes the responsiveness of quantity supplied to changes in market price Because price and quantity supplied are positively related, eS,P > 0

A Short-Run Supply Function
Suppose that there are 100 identical firms each with the following short-run supply curve qi (P,v,w) = 10P/3 (i = 1,2,…,100) This means that the market supply function is given by

A Short-Run Supply Function
In this case, computation of the elasticity of supply

Equilibrium Price Determination
An equilibrium price is one at which quantity demanded is equal to quantity supplied neither suppliers nor demanders have an incentive to alter their economic decisions An equilibrium price (P*) solves the equation: The equilibrium price depends on many exogenous factors changes in any of these factors will likely result in a new equilibrium price

Equilibrium Price Determination
The interaction between market demand and market supply determines the equilibrium price Price S Q1 P1 D Total output per period

Market Reaction to a Shift in Demand
If many buyers experience an increase in their demands, the market demand curve will shift to the right D’ Price S Q2 P2 Equilibrium price and equilibrium quantity will both rise P1 D Q1 Total output per period

Market Reaction to a Shift in Demand
q2 P2 If the market price rises, firms will increase their level of output Price SMC SAC This is the short-run supply response to an increase in market price P1 q1 Output per period

Shifts in Supply and Demand Curves
Demand curves shift because incomes change prices of substitutes or complements change preferences change Supply curves shift because input prices change technology changes number of producers change When either a supply curve or a demand curve shift, equilibrium price and quantity will change The relative magnitudes of these changes depends on the shapes of the supply and demand curves

Shifts in Supply Large increase in price, Small increase in price,
small drop in quantity Small increase in price, large drop in quantity Price S’ Price S’ S S P’ P’ P P D D Q’ Q Q per period Q’ Q Q per period Elastic Demand Inelastic Demand

Shifts in Demand Small increase in price, large rise in quantity
Large increase in price, small rise in quantity S Price Price S P’ P’ P P D’ D’ D D Q Q’ Q per period Q Q’ Q per period Elastic Supply Inelastic Supply

Mathematical Model of Supply and Demand
Suppose that the demand function is represented by QD = D(P,)  is a parameter that shifts the demand curve D/ = D can have any sign D/P = DP < 0 The supply relationship can be shown as QS = S(P,)  is a parameter that shifts the supply curve S/ = S can have any sign S/P = SP > 0 Equilibrium requires that QD = QS

To analyze the comparative statics of this model, we need to use the total differentials of the supply and demand functions: dQD = DPdP + Dd dQS = SPdP + Sd Maintenance of equilibrium requires that dQD = dQS

Suppose that the demand parameter () changed while  remains constant The equilibrium condition requires that DPdP + Dd = SPdP Because SP - DP > 0, P/ will have the same sign as D

We can convert our analysis to elasticities

Equilibria with Constant Elasticity Functions
Suppose the demand for automobiles is given by The supply for automobiles is

If I = $20,000 and w = $25 Equilibrium occurs where P* = 9,957 and Q* = 12,745,000

If I increases by 10 percent Equilibrium occurs where P* = 11,339 and Q* = 14,514,000

If instead w increases to $30 per hour Equilibrium occurs where P* = 10,381 and Q* = 12,125,000

Long-Run Analysis In the long run, a firm may adapt all of its inputs to fit market conditions profit-maximization for a price-taking firm implies that price is equal to long-run MC Firms can also enter and exit an industry perfect competition assumes that there are no special costs of entering or exiting an industry

Long-Run Analysis New firms will be lured into any market where economic profits are greater than zero the short-run industry supply curve will shift outward market price and profits will fall the process will continue until economic profits are zero

Long-Run Analysis Existing firms will leave any industry where economic profits are negative the short-run industry supply curve will shift inward market price will rise and losses will fall the process will continue until economic profits are zero

Long-Run Competitive Equilibrium
A perfectly competitive industry is in long-run equilibrium if there are no incentives for profit-maximizing firms to enter or to leave the industry this will occur when the number of firms is such that P = MC = AC and each firm operates at minimum AC

Long-Run Competitive Equilibrium
We will assume that all firms in an industry have identical cost curves no firm controls any special resources or technology The equilibrium long-run position requires that each firm earn zero economic profit

Long Run Market Equilibrium
A long run perfectly competitive equilibrium occurs at a market price, P*, a number of firms, n*, and an output per firm, q* that satisfies: 1) Long run profit maximization with respect to output and plant size: P* = MC at an output level q* 2) Zero economic profit P* = AC at an output level q* 3) Demand equals supply Qd depending on (P*) = n*q* …or… n* = {Qd depending on (P*)} / q*

Calculating Long Run Equilibrium
In the market, all firms and potential entrants are identical. Each has a total cost function given as: TC(q) = 40q - q q3 where q is measured in ‘000 units. The market demand curve is D(P): Qd(P) = P Find the following: Long run equilibrium quantity per firm Long run equilibrium price Number of firms.

Long Run Perfectly Competitive
$/unit $/unit Typical Firm Market n* = 10,000,000/50,000=200 MC Market demand SAC AC P* SMC q q*=50,000 Q*=10 Million Q

Long Run Market Supply Curve
We have calculated a point at which the market will be in long run equilibrium. This is a point on the long run market supply curve. Definition: The Long Run Market Supply Curve tells us the total quantity of output that will be supplied at various market prices, assuming that all long run adjustments (plant, entry) take place.

Long-Run Competitive Equilibrium: Derivation of LRIS curve
1) Constant cost industry 2) Increasing cost industry 3) Decreasing cost industry

1) Long-Run Equilibrium: Constant-Cost Case
Assume that the entry of new firms in an industry has no effect on the cost of inputs no matter how many firms enter or leave an industry, a typical firm’s cost curves will remain unchanged This is referred to as a Constant - Cost industry

Long-Run Equilibrium: Constant-Cost Case
This is a long-run equilibrium for this industry P = MC = AC Price Price MC SMC S AC P1 Q1 q1 D Quantity per period Quantity per period A Typical Firm Total Market

Suppose that market demand rises to D’ D’ P2 Market price rises to P2 Q2 Price Price MC SMC S AC P1 D q1 Quantity per period Q1 Quantity per period A Typical Firm Total Market

In the short run, each firm increases output to q2 q2 Economic profit > 0 Price Price MC SMC S AC P2 P1 D’ D q1 Quantity per period Q1 Q2 Quantity per period A Typical Firm Total Market

In the long run, new firms will enter the industry S’ Economic profit will return to 0 Q3 Price MC Price SMC S AC P1 D’ D q1 Quantity per period Q1 Quantity per period A Typical Firm Total Market

The long-run supply curve will be a horizontal line (infinitely elastic) at p1 LRIS Price MC Price SMC S S’ AC P1 D’ D q1 Quantity per period Q1 Q3 Quantity per period A Typical Firm Total Market

Infinitely Elastic Long-Run Supply
Suppose that the total cost curve for a typical firm in the bicycle industry is C(q) = q3 – 20q q + 8,000 Demand for bicycles is given by QD = 2,500 – 3P Calculate Long run equilibrium quantity per firm Long run equilibrium price Number of firms. If the demand increases to QD = 3,000 – 3P

2) Long-Run Equilibrium: Increasing-Cost Industry
The entry of new firms may cause the average costs of all firms to rise prices of scarce inputs may rise new firms may impose “external” costs on existing firms new firms may increase the demand for tax-financed services

Long-Run Equilibrium: Increasing-Cost Industry
Suppose that we are in long-run equilibrium in this industry P = MC = AC Price MC SMC Price S AC P1 D q1 Quantity per period Q1 Quantity per period A Typical Firm (before entry) Total Market

Suppose that market demand rises to D’ D’ P2 Market price rises to P2 and firms increase output to q2 Q2 q2 MC Price SMC Price S AC P1 D q1 Quantity per period Q1 Quantity per period A Typical Firm (before entry) Total Market

Positive profits attract new firms and supply shifts out S’ q3 P3 Entry of firms causes costs for each firm to rise Q3 Price SMC’ MC’ Price S AC’ P1 D’ D Quantity per period Q1 Quantity per period A Typical Firm (after entry) Total Market Total Market

The long-run supply curve will be upward-sloping LRIS SMC’ Price MC’ Price S S’ AC’ p3 p1 D’ D q3 Quantity per period Q1 Q3 Quantity per period A Typical Firm (after entry) Total Market

Increasing Cost Industry
Increasing cost Industry: An industry which increases in industry output increase the price of inputs. Especially if firms use industry specific inputs i.e. scarce inputs that are used only by firms in a particular industry and no other industry.

Long-Run Equilibrium: Decreasing-Cost Industry
The entry of new firms may cause the average costs of all firms to fall new firms may attract a larger pool of trained labor entry of new firms may provide a “critical mass” of industrialization permits the development of more efficient transportation and communications networks

Suppose that we are in long-run equilibrium in this industry P = MC = AC Price MC Price SMC S AC P1 D q1 Quantity per period Q1 Quantity per period A Typical Firm (before entry) Total Market

Suppose that market demand rises to D’ D’ P2 Market price rises to P2 and firms increase output to q2 Q2 q2 Price MC SMC Price S AC P1 D q1 Quantity per period Q1 Quantity per period A Typical Firm (before entry) Total Market

Positive profits attract new firms and supply shifts out S’ P3 Entry of firms causes costs for each firm to fall Q3 q3 Price Price SMC’ MC’ S AC’ P1 D’ D q1 Quantity per period Q1 Q1 Quantity per period A Typical Firm (before entry) A Typical Firm (before entry) Total Market

The long-run industry supply curve will be downward-sloping Price Price SMC’ S MC’ S’ AC’ LRIS P1 P3 D D’ q1 q3 Quantity per period Q1 Q3 Quantity per period A Typical Firm (before entry) Total Market

Decreasing Cost Industry
Decreasing-cost Industry: An industry in which increases in industry output decrease the prices of some or all inputs.

Long-Run Elasticity of Supply
The long-run elasticity of supply (eLS,P) records the proportionate change in long-run industry output to a proportionate change in price eLS,P can be positive or negative the sign depends on whether the industry exhibits increasing or decreasing costs

Comparative Statics Analysis
Comparative statics analysis of long-run equilibria can be conducted using estimates of long-run elasticities of supply and demand 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 Q0 and the typical firm’s output is q* (where AC is minimized) The equilibrium number of firms in the industry (n0) is Q0/q*

A shift in demand that changes the equilibrium industry output to Q1 will change the equilibrium number of firms to n1 = Q1/q* The change in the number of firms is determined by demand shift and the optimal output level for the typical firm

The effect of a change in input prices is more complicated 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 The optimal level of output for each firm may also be affected Therefore, the change in the number of firms becomes

Rising Input Costs and Industry Structure
Suppose that the total cost curve for a typical firm in the bicycle industry is C(q) = q3 – 20q q + 8,000 and then rises to C(q) = q3 – 20q q + 11,616 The optimal scale of each firm rises from 20 to 22 (where MC = AC)

Rising Input Costs and Industry Structure
At q = 22, MC = AC = $672 so the long-run equilibrium price will be $672 If demand can be represented by QD = 2,500 – 3P then QD = 484 This means that the industry will have 22 firms (484  22)

Producer Surplus in the Long Run
Short-run producer surplus represents the return to a firm’s owners in excess of what would be earned if output was zero the sum of short-run profits and fixed costs In the long-run, all profits are zero and there are no fixed costs owners are indifferent about whether they are in a particular market

Producer Surplus in the Long Run
Long-run producer surplus is the extra return that producers make by making transactions at the market price over and above what they would earn if nothing were produced the area above the long-run supply curve and below the market price

Producer Surplus P Market Supply Curve P* Producer Surplus Q

Ricardian Rent Assume that there are many parcels of land on which a particular crop may be grown the land ranges from very fertile land (low costs of production) to very poor, dry land (high costs of production) At low prices only the best land is used Higher prices lead to an increase in output through the use of higher-cost land the long-run supply curve is upward-sloping because of the increased costs of using less fertile land

Ricardian Rent The owners of low-cost firms will earn positive profits
Price Price MC AC S P* D q* Quantity per period Q* Quantity per period Low-Cost Firm Total Market

Ricardian Rent The owners of the marginal firm will earn zero profit
Price Price MC AC S P* D q* Quantity per period Q* Quantity per period Marginal Firm Total Market

Economic Rent Economic Rent: The economics rent that is attributed to extraordinarily productive inputs whose supply is scarce. Difference between the maximum value is willing to pay for the services of the input and input’s reservation value. Reservation value: The returns that the owner of an input could get by deploying the input in its best alternative use outside the industry.

Economic Rent Economic rent is the shaded area
Each point on the supply curve represents minimum average cost for some firm For each firm, P – AC represents profit per unit of output

The Partial Equilibrium Competitive Model

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