Advanced Microeconomics · 2019-01-17 · In the long-run market equilibrium, the market price is...

Advanced Microeconomics

Ivan Etzo

University of Cagliari

[email protected] in Scienze Economiche e Aziendali, XXXIII ciclo

Ivan Etzo (UNICA) Lecture 5: Supply 1 / 32

Overview

1 Market Environments

2 Pure Competition

3 The demand curve of a competitive firm

4 The firm’s Short-Run Supply Curve

5 The firm’s Long-Run Supply Curve

6 Industry Supply

7 Long-Run Industry Equilibrium


Market Environments

A firm faces two main decisions:1 Choosing how much it should produce;2 Choosing what price to set.

The choice is not free.

As we have seen, the firm faces the technological constraint (thefeasible production possibilities) summarized by the productionfunction.

The technological constraint implies also some economicconstraints summarized by the cost function.

A further important constraint is the market constraint.

In short, the market constraint says that the firm can only sell asmuch as people are willing to buy.


Market Environments

The demand curve facing the firm describes the relationshipbetween the price a firm sets and the quantity it sells.

Remember that the demand curve facing the firm IS NOT the marketdemand curve, unless the firm is the only one in the market.

If there are other firms in the market then the choices of the singlefirm is affected by the choices made by the other firms.

The market environment describes how the firms respond to eachother when they make their pricing and output decisions.


Market Environments

Monopoly: Just one seller that determines the quantity supplied andthe market-clearing price.

Oligopoly: A few firms, the decisions of each influencing the payoffsof the others.

Monopolistic Competition:Many firms each making a slightlydifferent product. Each firm’s output level is small relative to thetotal.

Pure Competition: Many firms, all making the same product. Eachfirm’s output level is small relative to the total.


Pure Competition

The Pure Competition is a market environment where each firmassumes that the market price does not depend on its own level ofoutput.

In other words, the firm is left with the only decision of how much toproduce because whatever amount will be sold at the (fixed) marketprice.

Usually, is an industry composed of many small firms, where smallmeans that their supply represents a negligible share of the marketsupply.

Each firm is a price taker, the single firm cannot decide the pricelevel.

The product produced by each firm is the same (homogeneousproduct).


The demand curve of a competitive firm

In pure competition the demand curve facing the firm is differentfrom the market demand curve.

The demand curve facing the firm measures the relationship betweenthe market price and the output level of that particular firm.

The market demand curve depends on consumers’ behavior.


The demand curve of a competitive firmThe demand curve of the single firm



When p = p′ the quantity supplied by the single firm is y = 0.Ivan Etzo (UNICA) Lecture 5: Supply 9 / 32


When p = p′′ the firm faces the all market.Ivan Etzo (UNICA) Lecture 5: Supply 10 / 32




This is the demand curve facing a single firm in pure competition.Ivan Etzo (UNICA) Lecture 5: Supply 12 / 32

The firm’ supply curve

The profit maximizing problem is the following:

maxy

py − c(y)

where the price p is constant and c(y) is the cost function.

The first-order and the second-order conditions are the following:

FOC : p = c ′(y∗)

SOC : −c ′′(y∗) ≤ 0 ⇒ c ′′(y∗) ≥ 0

The FOC says that the price equals marginal cost and the SOC saysthat the marginal cost must be increasing.

Thus, the supply function is given by the FOC:

p = MC (y)


The firm’ supply curveThe shutdown decision point

The firm can always decide to produce zero units of output. In orderto produce y > 0 it must be that:

π(y > 0) ≥ π(y = 0)

py − cv (y)− FC ≥ −FC

where −FC are the profits when the firm produce zero units of output.

Rearranging we get

p ≥ cv (y)

y

That is, the price must be greater than the average variable costs.

Therefore, the supply curve is only the segment of the MC curve lyingabove the AVC curve.


The firms Short-Run Supply Curve


The inverse supply function

The direct supply function is the output as a function of the price.

On the opposite, the inverse supply function is the price as afunction of the output level.

According to the FOC of the profit maximizing problem the inversesupply function is the following:

P = MC (y)

So, every firm in the market must have the same marginal cost (ifthey are all maximizing profits).


The firm’s Long-Run Supply Decision

A competitive firm’s long-run profit function is:

π(y) = py − c(y)

The long-run cost c(y) of producing y units of output consists only ofvariable costs, since all inputs are variable in the long-run.

That is, the long-run supply curve can be written as:

p = MCl(y) = MC (y , k(y))

where k is the factor that is fixed in the short-run (e.g. plant size).

Thus, in the long run the firm can adjust the fixed factor optimally tothe output level.

Remember that the short-run and the long-run marginal costscoincide at the level of output y∗, where the fixed factor choiceassociated with the short-run marginal cost is the optimal choice k∗.



In the long-run equilibrium profits cannot be negative because thefirm would go out of business otherwise:

py − c(y) ≥ 0

or, equivalently

p ≥ c(v)

y

Thus, in the long-run price must be at least as large as average cost.

The long-run supply curve is more elastic than the short-run supplycurve. That is, the firm is more responsive to price because all factorscan be adjusted.




Short-Run and Long-run Supply Curve



where, y∗s is profit-maximizing in the short-run and y∗ is profit-maximizing in thelong-run.












Industry Supply

Since every firm in the industry is a price-taker, total quantitysupplied at a given price is the sum of quantities supplied at thatprice by the individual firms.

Therefore, the industry (o market) supply curve is

S(p) =n∑

i=1

si (p)

where, S(p) indicates the industry supply, si (p) is the supply of thesingle firm and n is the number of firms.


Short-Run Industry Equilibrium

In the short-run, neither entry nor exit can occur.

Consequently, in a short-run equilibrium, some firms may earn positiveeconomic profits, others may suffer economic losses, and still othersmay earn zero economic profit.








Long-Run Industry Equilibrium

free entry assumption: in pure competition there are no barriers toentry such as licenses, patents or legal restrictions on the number offirms.

Therefore, in the long-run every firm now in the industry is free toexit and firms now outside the industry are free to enter.

Positive economic profit induces entry.

Entry increases industry supply, causing pes to fall.

How many firms will enter?

The long-run number of firms in the industry is the largest number forwhich the market price is at least as large as min AC(y).

In the long-run market equilibrium, the market price is determinedsolely by the long-run minimum average production cost.

Pe = miny>0

AC (y)

Thus, in the long-run equilibrium the (economic) profit is zero.


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Advanced Microeconomics · 2019-01-17 · In the long-run market equilibrium, the market price is...

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