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McPeak Lecture 10 PPA 723
The competitive model.
Marginal willingness to pay (WTP). The maximum amount a consumer will spend for an extra unit of the good.
As we derived a demand 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 given quantity of good and what the good costs.
[show graph]
Relies on the fact that the demand curve is downward sloping and that the price for purchasing is the same for all units.
The area under the demand curve and above the price line.
The area below the price line is expenditure (p times q).
If price increases and demand is constant, consumer surplus falls.
The decrease in consumer surplus for a given price increase will be larger:
The greater the initial expenditure on the good
The less elastic is the demand curve.
Producer surplus. The difference between the minimum amount necessary for the seller to be willing to produce the good and the selling price.
[show graph]
Producer surplus is revenue minus variable cost. Since profit 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.
Monopoly. There is only one supplier of a good for which there is no close substitute.
How can such a thing happen?
Technical reasons. a. Economies of scale. A natural monopoly exists 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. Large Sunk costs.
Legal reasons. a. Patents. b. Franchises c. Legal barriers.
Marginal revenue as you 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 firm 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]
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10
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(^1357911131517192123)
Price Discrete MR Bisection MR
Price TR
Discrete MR
Bisection MR 1 23 23 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
Profit maximization steps for the monopolist.
- Identify q^ that determines where MR(q)= MC(q*)
- Calculate what is the implied p^ for that q^ from the demand curve.
- Calculate profit which is defined by p^ times q^ minus cost at q*
- Shut down (produce q=0) if p*^ is less than average variable cost (SR) or average cost (LR).
Simple example.
Demand is defined by p=24-q, and total cost is defined by TC=q^2 , so that MC = 2*q (you will be given this, not be expected to derive it).
If we know that p=24-q, we can use the bisection rule to define MR=24-2q, since R=pq, =24q- q^2.
Where is MR=MC?
Where is 24-2q=2q, 24=4q, or q=6.
At a quantity of six, I plug back into the demand curve and find that p=24-6, or 18.
[note: a common mistake is to plug back into MR curve to solve for price]
Profit for me at this point is revenue minus cost, or 186- 66, or 72.
To make life easier on us, I will tend to give you a constant marginal cost, but the procedure is the same.
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=2 when q=11, which is where p=13. In perfect competition by contrast, 24-q=2 when q=22, so that p=2.
PS with perfect competition is the area below the price line and above the supply curve = 0.
PS with monopoly is the area defined by: (pmonopoly-mc)(q monopoly), or (13-2)11 =
CS with perfect competition is the area above the competition price line and below the demand curve, a triangle. When q=0, p=24 by the demand curve. So we have (pwhen q=0-pcompetition)(qcompetition)(1/2)=(24- 2)22(1/2)=
CS with monopoly is the area above the monopoly price line and below the demand curve, a triangle. (pwhen q=0- pmonopoly)(qmonopoly)(1/2)=(24-13)11(1/2)=60 ½.
Total welfare under competition is 0+242= Total welfare under monopoly is 121+60 ½, or 180.
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?
- Optimal price regulation, which sets a price ceiling.
What would the equilibrium market clearing price quantity pair be if the market was competitive? Set the price ceiling 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 pair.
[show graph]
[show graph when the price ceiling is set too low]
