Lecture Notes

Monopoly Market environment where there is only

one firm in the market Firm faces ALL of demand So monopoly profit = p(y)y – c(y) Where p(y) = inverse market demand let p(y)y

= r(y) revenue function Monopolistic problem: Choose y to Max r(y) – c(y) First order conditions are given by: MR = MC

The same condition we got with perfect competitionBut now MR does not equal P (i.e. firms not

price takers)

Two effects of changing y (say increase y) on revenues 1-sell more so revenue increases 2-price decreases so revenue decreases

∆ r (y) = p ∆y + y ∆p ∆ r(y)/ ∆ y = MR = p + y ∆p/ ∆y or: For price takers ∆p=0 => ∆r = p ∆y But now P decreases as y increases so the second

term matters.

Now both 1 and 2 measure Marginal Revenue (MR)MR= ∆r/ ∆y = p + y ∆p/ ∆y= p(1 + (y/p)(∆p/ ∆y)= p(y) (1 + 1/ε) Since ε = price elasticity of demand = (p/y)(∆y/∆p)=> can re-write optimal condition, MR = MC as:

p(y) (1 + 1/ ε(y)) = mc (y)Or p(y) (1- 1/| ε(y)|) = mc (y)

Since ε < 0 Also recall that | ε | > 0 elastic | ε | < 1 inelastic So that if demand elastic regions | ε | > 1 MR > 0 but if demand inelastic MR < 0

The above implies that the Monopolist only operates in elastic portion of Demand since MR < 0 when demand inelastic and profit max. requires

MR = MC but MC < 0 is unlikely (impossible).

Now with linear demand…P(y) = a –b ySo R (y) = ay –by2 => MR= a – 2byNotice 3 things:

1. MR = D at y=0 2. slope of MR = 2 times the slope of demand (i.e., twice

as steep). 3. MR = 0 where | ε | = 1 (this is always true not just for

linear Demand)

Look at tax example: suppose c(y) = cy=> mc = c P(y) = a-by so MR = a -2by

MC

AC

MR

Ym y

Pm

D

Now suppose a tax on the monopolist = t (quantity tax) so pc = ps + t

So mc w/ tax is c + t or c(y) = (c+ t)y=> before profit max where c = a -2byOr y* = a-c/2bNow MC = c + t = a – 2by = MRSo y* = (a-c-t)/2b=> Δy/ Δ t = -1/(2b) (why?)What is the impact of the tax on price, p?

Recall slope of demand function = Δp/ Δy = -b, so The tax is imposed => y changes by -1/(2b) then The price changes by – b, the overall impact is both of these

together, Or – b times -1/(2b) = -1/2

Interpretation: if t increases by $1 => price increases by $.50

But note that p may actually increase more than by the amount of tax. See book for example

Yt y*

C + t

MC = C

pt

P*

MR D

Now look at efficiency and compare to perfect competition

Again assume MC = C (constant returns) in the long run Produce at (pm, ym)

Ym yc

MC=LRAC

Pm

Pc=c

MR D

Deadweight loss to society

But competitive firms would produce at MC = D Or (pc, yc) which is the point that maximizes net surplus to society.

Or if upward sloping LRMC

Ym yc

Pm

Pc

MR D

Deadweight loss to society

MC

=> appears that monopolist is inefficient (i.e. does not max society’s net surplus)

Public policy: may be to get rid of monopolies(1) contestable markets i.e. free entry => if

profit > 0 more firms enter so profit = o even with one firm.

(2) economies of scale and scope Consider natural monopoly (economies of scale)

LRMC

LRAC

Pm

Pt

YmMR D

Only one firm can cheaply produce given demand but (1) if p=mc=Pso(socially optimum price)

Firms makes a loss and leaves (2) if p=pm => deadweight loss (3) if p=AC=pf (fair price) still a loss in profit but

firm can operate But if break up of monopoly:

Pc > Pm > Pf >Pso => competition is not more efficient due to economies of scale.

Same may to be true due to economies of scope.

Price Discrimination3 different types

A. Perfect price discrimination—price the monopolists sells is just equal to your willingness to pay => With no price discrimination produce at (pm, ym)

but this assumes no ability to discriminate

Now perfectly discriminate => D=MR and produce at Yc which is efficient (assuming $1 to producer is the same as $1 to consumer since CS=0)

Pm

Pe

Ym Ye

D

MC

MR

2nd degree Price Discrimination Pi= f(yi) i.e. how much you pay depends on your

consumption Examples: utilities, bulk discounts for large

purchases3rd degree price discrimination-different groups

get different prices but individuals within a group get the same price

Most common type: Examples 1. movie theatre discounts (kids v. adults) 2. local ski discounts (locals v. non-locals) More formally suppose 2 groups with different

demand => max P1 (Y1) Y1 + P2 (Y2) Y2 – C(Y1 + Y2) by:

MR1 – MC(Y1 + Y2) = 0 MR2 – MC(Y1 + Y2) = 0

Combine to get MR1 = MC(Y1 + Y2) = MR2 orP1 [1- 1/| ε1 |] = MC (Y1 +Y2) = P2 [1-1/| ε 2|]

If P1 > P2 => [1-1/| ε 1|] < 1 – 1/| ε 2| or

1/| ε 1| > 1/| ε 2| or | ε 2| > | ε 1|i.e. for P1 > P2 demand for group 1 must be

more inelasticGraphically, assume C= MC

C

Y1

P1

C

Group 1

D1

MR1

Y2

P2

Group 2

D2MR2

Innovation—monopolies have more incentive to innovate (at least this is the argument)

Define innovationJust a decrease in MC to MC2 assuming

constant returnsP

Q

MC1

MC2

What are the incentives to innovate for monopoly?

I.e. increase profit due to innovation = shaded area. Why?

P

Y

MC1

MC2

DMR

What are incentives to innovate for perfectly competitive industry?

None unless (1) innovative technology is secret or (2) a patent system exists

Under a patent system what is the incentive? What are increased profits to patent holder?

1st what does patent holders MR curve look like? As long y < y* MR = C ; i.e. he’s a price taker.

P

Q

MC1

MC2

Y*

D

C

C1

But if y > y* the firm becomes sole supplierR= p(y)y so MR is downward sloping and

determined by D when y > y*.Note: as long as C > C* ; y = y* in the market.

This is a small innovation. But if C < C* so y > y* then this is a large

innovation.

MR

P

Y

C

C1

C*

Y*

D

Now just look at a small innovation (i.e. y = y* before and after innovation)

MR

P

Y

C

C2

D

Notice that the incentive to innovate for a competitive industry is greater than for a monopoly because output is larger for the competitive firm.

Incentive to innovate to competitive industry

Q: What if economies of scale in innovation (i.e. small firms in competitive industry don’t have resources to innovate)

A: Firms specialize in innovating, gain patents and license to small competitive firms Example: agriculture where innovating is done by

Universities Seed companies Etc.

Monopolistic CompetitionCharacteristics

Large numbe r of potential sellers All small relative to market Differentiated product Easy entry and exit

The short-run looks like a monoply

Ym

Pm

MR

D

MC ATCProfit

Profit can also be negative or zero in the short-run. If negative => firms exit if p< avc.

Long-run equilibrium is just like for competition:If profit > 0 => entry which drives profit down.If profit < 0 => exit which drives profit up.Therefore, long-run equilibrium is where profit

equals zero, where no exit or entry.

PoPc

Qo Qc

MR

D

MC ATC

Notice that at Equilibrium but P > MC Resource Allocation & Efficiency

Since MSC does not equal MSB or MSB > MSC => inefficient p.c. firm would produce the efficient amount.

Might be efficient if benefit from different products > Cost of producing different products

=> in long run (1) each firm is on its demand curve (2) each firm chooses y to max profit (3) entry forces profit = 0 (4) P > MC => inefficient