Competitive Firms in the Long-Run - blogs.uoregon.edu face the LMC curve The rm would choose to produce q 3 in the long-run because ... EC 311 - Selby Competitive Firms in the Long-Run

Competitive Firms in the Long-Run

EC 311 - Selby

May 18, 2014

EC 311 - Selby Competitive Firms in the Long-Run May 18, 2014 1 / 20

Recap

So far we have been discussing the short-run for competitive firms

The firms want to maximize their short-run profits. Since they areprice-takers, they face the following problem

maxqπ(q) = R(q)− C (q) = Pq − C (q)

The profit maximizing level of output always satisfies the condition

P = MC (q∗)


If P > ATC the firm is making positive short-run profit

if P = ATC the firm is breaking even

if P < ATC the firm is making short-run losses

if P < AVC the firm must shut down

Knowing this then the firm’s supply curve is

qS =

{0 : P < AVCMC−1(P) : P ≥ AVC

We can find the market supply curve by adding up the individualsupply curves horizontally

The elasticity of supply for the market is

ES =∂QS

∂P

P

QS


Short-run producer surplus can be found as the area between theprice and the marginal cost of producing up to q∗

We can calculate producer surplus as

PS = R(q∗)− VC (q∗) = (P − ATC (q∗))q∗

We can also calculate it based on profits:

PS = π(q∗) + FC

What if the firm wants to change it’s production process to increaseprofits?

In the short-run, some factors are fixed and so they cannot adapt totechnological improvements or change it’s scale of operation.

However, when we look at the long-run things are much more flexible.


Choosing Output in the Long-Run

Recall that in the long-run, a firm faces a long-run average cost curvethat envelopes the short-run average cost curves


The point at which LMC = LAC , is where long-run average costs areminimized.

Price is not necessarily going to be at this point.


In the short-run, if P = 40, they would choose to produce q1 becausethat is the point where P = SMC .

At q1, the firm is making short-run profits

π = (40− C ) ∗ q1

In the long-run, they can adapt their production process and theywould face the LMC curve

The firm would choose to produce q3 in the long-run becauseP = LMC .

At q3 the firm would make long-run profits

πLR = (40− G ) ∗ q3

Which is bigger: long-run or short-run profits?

What is their profits if P = 30?


Long Run Competitive Equilibrium

Now that we have discussed profit maximizing choices in the long andshort-run

What do we expect to occur in a long-run equilibrium?We are in a long-run competitive equilibrium when the followinghold:

1 All firms in the industry are profit maximizing2 No firm has the incentive to enter or exit because all firms are earning

zero economic profit (that is, they are getting returns that are just asbig as what they could get by investing elsewhere)

3 The price of the product is such that the quantity supplied by theindustry is exactly equal to the quantity demanded by consumers


Suppose that firms have identical costs. If, for example, the cost ofcapital dramatically decreases, then firms will make positive economicprofit.

I If too many firms enter the market responding to a chance of profit,the supply curve will shift right and price will fall

I At this lower price, some firms will incur losses and supply will shift left.I Firms will continue to do this until we end up at the new long run

supply curve.

A firm will exit the market if it faces long-run loss, or P < LAC


Consider the firm from earlier:


This firm is making positive economic profits.

If this firm is representative, then all of the firms face the same costsand everyone in the market is making positive profits.

As new firms enter the industry seeking this profit, then the marketsupply curve shifts right and the price drops.

The price drops to the point where P = LAC for the firms in theindustry.



Example: Suppose we know the following

QD = 6500− 100P Market DemandQS = 1200P Market Supply

C (q) = 722 + q2

200 Firm TCMC (q) = q

100 Firm MC

What is the equilibrium price and quantity supplied?

In equilibrium, condition (3) gives us that

QD = QS

=⇒ 6500− 100P = 1200P

=⇒ 6500 = 1300P

=⇒ P = 5

=⇒ Q = 6500− 100(5) = 6000


We now know that market price is P = 5, what output does the firmproduce?

I If the firm is profit maximizing, then

P = MC (q)

=⇒ P = 5 =q

100= MC

=⇒ q = 500

What is the firm’s profit?

π(q) = Pq − C (q)

π(500) = 5(500)−(

722 +5002

200

)= 528

Do you expect firms to enter this market or exit?

What effect will this have on the the market?


Industry Long-Run Supply

When discussing market supply in the short-run, we could simply addup quantity supplied by each firm as price increases.

However, in the long run, when firms enter and exit the market, themarket price changes.

The long-run supply depends on how output affects the prices thatfirms must pay for inputs

I Economies of scale: input prices decline with outputI Diseconomies of scale: input prices increase with outputI Neither: input prices do not change with output

This leads to three possible outcomes for the supply curve


Case 1: Constant-Cost Industries

A constant cost industry is an industry whose long-run supply curveis horizontal

Consider the following figure:


Originally the market price is P1 and is set by demand curve D1 andshort-run supply curve S1

A typical firm in this market has constant-costs. That is, when pricesof output go up, the AC curve does not change.

When P = P1, the firm produces q1

Suppose that there is a sudden increase in demand and the demandcurve shifts to D2

In the short-run, prices will go up to P2 and the typical firm will bemaking positive economic profits.

This induces firms to start entering the market. They will continue todo so until the price is driven back down to P1.

This results in an increase in supply and the short-run supply curveshifts to S2

Explanation? Neither economies or diseconomies of scale. There is nochange in input prices with a change in scale.


Case 2: Increasing-Cost IndustryAn increasing-cost industry is an industry whose long-run supplycurve is upward slopingAs new firms enter the market, increased demand for inputs causessome/all of input prices to increase, resulting in increased AC for thetypical firmConsider the following figure:


Suppose we have the same demand increase as before.

When prices go up to P2, firms start entering the market

This causes input prices to increase. This shifts the MC curve left(more expensive to produce the same level of output). This also shiftsthe AC upward.

This leads to an increase in supply, but not as much as under theconstant cost situation. The supply curve shifts from S1 to S2 andlands a new higher market price of P3 (it must be higher due tohigher input costs - zero economic profit)

The long-run supply curve for this industry is upward-sloping.

Explanation? Diseconomies of scale. There is increasing input costwith increasing scale.


Case 3: Decreasing-Cost Industry

A decreasing-cost industry is an industry whose long-run supplycurve is downward sloping.

As firm’s enter the market, input prices decline.

This leads to the opposite of what happens in the previous case.

What does this look like graphically?

What might be a possible explanation?


Documents

Competitive Firms in the Long-Run - blogs.uoregon.edu face the LMC curve The rm would choose to produce q 3 in the long-run because ... EC 311 - Selby Competitive Firms in the Long-Run