PPA 723 Lecture 10

McPeak

Lecture 10=

PPA 723

T= he competitive model.

M= arginal willingness to pay (WTP). The maximum amount a consumer will= spend for an extra unit of the good.

As we derived a deman= d curve for an individual’s preferences, we can interpret the demand curve tracing out the consumer’s marginal willingness to pay at different levels of consumption.

Consumer surplus (CS)= – the monetary difference between what the consumer is willing to pay for a g= iven quantity of good and what the good costs.&= nbsp;

[show graph]

R= elies on the fact that the demand curve is downward sloping and that the price for purchasing is the same for all units.

T= he area under the demand curve and above the price line.

The area below the pr= ice line is expenditure (p times q).

If price increases an= d demand is constant, consumer surplus falls.

The decrease in consu= mer surplus for a given price increase will be larger:

· The greater= the initial expenditure on the good

· The less el= astic is the demand curve.

P= roducer surplus. The difference= between the minimum amount necessary for the seller to be willing to produce the go= od and the selling price.

[show graph]

Producer surplus is r= evenue minus variable cost. Since pr= ofit is revenue minus cost, the difference between profit and producer surplus is fixed cost in the short run, and there is no difference in the long run.

The maximum societal = welfare comes from maximizing consumer surplus plus producer surplus.

Why are there gains t= o trade?

[show graph of when quantit= y is too low]

[ show graph of when quanti= ty is too high]

M= onopoly.

There is only one sup= plier of a good for which there is no close substitute.

How can such a thing = happen?

1)&n= bsp; Technical reasons.

a.&n= bsp; Economies of scale. A natural monopoly exi= sts when one firm can produce at a lower cost than several firms producing the = same good and total output level (AC is downward sloping over the feasible range= of output).

b.&n= bsp; Large Sunk = costs.

2)&n= bsp; Legal reaso= ns.

a.&n= bsp; Patents.

b.&n= bsp; Franchises<= o:p>

c.&n= bsp; Legal barriers. <= /p>

Marginal revenue as y= ou recall is the change in revenue divided by the change in q. In the competitive model, the price taking firm faced a marginal revenue of p, since= price did not change with the output level of the firm.

Now, the monopoly fir= m faces the entire demand curve. This= is downward sloping, so by picking a level of q, there is also an associated p (the whole demand curve is defined by (p,q) pairs).

[= show graph]

<= o:p>	P= rice	T= R	D= iscrete MR	B= isection MR
1	23	23	<= o:p>	<= o:p>
2	22	44	21	20
3	21	63	19	18
4	20	80	17	16
5	19	95	15	14
6	18	108	13	12
7	17	119	11	10
8	16	128	9	8
9	15	135	7	6
10	14	140	5	4
11	13	143	3	2
12	12	144	1	0
13	11	143	-1	-2
14	10	140	-3	-4
15	9	135	-5	-6
16	8	128	-7	-8
17	7	119	-9	-10
18	6	108	-11	-12
19	5	95	-13	-14
20	4	80	-15	-16
21	3	63	-17	-18
22	2	44	-19	-20
23	1	23	-21	-22
24	0	0	-23	-24

Note there is a diffe= rence between calculating the MR from one observation to the next compared to the= MR at a given point.

B= isection rule. Marginal revenue for a linear dema= nd curve defined by: p=3Da-b*q is MR=3Da-2*b*q.

For a linear demand c= urve, the marginal revenue curve bisects the demand curve.

Why?

Well demand is (24-q<= span class=3DGramE>)=3Dp in the example above, and we know p*q is revenue= . So p*q is the same as (24-q)*q, or= 24q-q². The marginal of this is the deriva= tive with respect to q, or 24-2q.

The competitive firm choose q given p. Here, the monopoly chooses p and q based on information about the en= tire demand curve. It is making its choices in the awareness that increasing q decreases price, and that margin= al revenue is a function of the quantity they pick.

Profit maximization s= teps for the monopolist.

1)&n= bsp; Identify q<= sup>* that determines where MR(q^*)=3D MC(q^*)

2)&n= bsp; Calculate w= hat is the implied p^* for that q^* from the demand curve.

3)&n= bsp; Calculate p= rofit which is defined by p^* times q^*minus cost at q^*=

4) Shut down (produce q=3D0) if p^* is le= ss than average variable cost (SR) or average cost (LR).

S= imple example.

Demand is defined by = p=3D24-q, and total cost is defined by TC=3Dq², so that MC =3D 2*q (you wi= ll be given this, not be expected to derive it).

If we know that p=3D2= 4-q, we can use the bisection rule to define MR=3D24-2*q, since R=3Dp*q, =3D24q- q<= sup>2.

Where is MR=3DMC?

Where is 24-2*q=3D2*q= , 24=3D4q, or q=3D6.

At a quantity of six,= I plug back into the demand curve and find that p=3D24-6, or 18.=

[= note: a common mistake is to plug back i= nto MR curve to solve for price]

Profit for me at this= point is revenue minus cost, or 18*6-6*6, or 72.

To make life easier o= n us, I will tend to give you a constant marginal cost, but the procedure is the sa= me.

How does this differ = from a perfectly competitive market in terms of outcome?

If we use the given d= emand curve and recall that the MC curve traces out the supply curve in a perfect= ly competitive market, we find:

24-q=3D2q where suppl= y and demand meet at a (p,q) pair, which solves for q^*=3D8, implying that p^*=3D16.

[show on graph]

There is a deadweight= loss of monopoly. The market structure makes it so that transactions that would occur in a perfectly competitive market do no occur, thus reducing total societal welfare.

Note efficiency / equ= ity distinction.

Now we can modify the example.

If we assume perfect competition and the conditions for a horizontal supply curve discussed last class, we can define a cost curve as 2*q, so the MC is a constant 2.

24-2q=3D2 when q=3D11= , which is where p=3D13.

In perfect competitio= n by contrast, 24-q=3D2 when q=3D22, so that p=3D2.

PS with perfect compe= tition is the area below the price line and above the supply curve =3D 0.

PS with monopoly is t= he area defined by: (p^monopoly-mc)*(q ^monopoly), or (13-2)*11 =3D121

CS with perfect compe= tition is the area above the competition price line and below the demand curve, a triangle. When q=3D0, p=3D24 = by the demand curve. So we have (p^when^q=3D0-p^{competition)*(q^competition)*(1/2)=3D=
(24-2)*22*(1/2)=3D242}

CS with monopoly is t= he area above the monopoly price line and below the demand curve, a triangle. (p^when^q=3D0-p^monopoly)*(q^monopoly)*(1/2)=3D(24-13)*11*(1/2)=3D60 ½.<= /p>

Total welfare under competition is 0+242=3D242

Total welfare under m= onopoly is 121+60 ½, or 180.5

This illustrates a general result – total welfare is reduced under monopoly market structure compared to a perfectly competitive market.

So what can we do about a monopoly?

1) Optimal pri= ce regulation, which sets a price ceiling.&nb= sp;

What would the equilibrium market clearing price quantity pair be if the market = was competitive? Set the price ce= iling at this level, so that the demand curve facing the monopolist is modified to have a flat spot, then decrease after passing to the right of this p, q pai= r.

[show graph]

[show graph when the price ceiling is set too low]

This is very difficult to get right if you don’t know the actual demand and cost curves.

Also may have a natural monopoly that is defined by decreasing average costs over the total range of feasible output levels. This means MC is below= AC over this range as well, since if AC is downward sloping, that means MC is = below it.

A policy that sets the price ceiling based on the marginal cost curve would m= ake it better for the monopolist to shut down rather than produce (thus losing whatever consumer and producer surplus we are getting under the monopoly situation).