- Consider a market where demand is of the following form: P(x)=200-2x. Suppose too, that there are constant marginal costs of 20
| Demand function: | P(x) = 200 – 2x | where, x = Number of units |
| Marginal costs are constant at 20 | P = Price per unit |
In a competitive model, Marginal Revenue equals Marginal Cost.
We already know that Marginal Cost is constant at 20. Therefore, the Marginal Revenue has the same equation, which is the Supply equation.
P=MR = MC = 20
Given a linear demand curve in inverse form, P = 200-2x.
- What will be the competitive outcome in terms of quantity produced and price?
SAMPLE ANSWER:
The market equilibrium, or the competitive output is at the point where Supply = Demand, which is:
| x = | 90 |
| P = | 20 |
- What will be consumer and producer surplus at this point?
- What would be the outcome had the market been dominated by a single producer?
| Demand function: | P(x) = 200 – 2x | where, x = Number of units | ||
| Marginal costs are constant at 20 | P = Price per unit |
Hence, Marginal Revenue curve: MR = 200 – 4x
We already know that Marginal Cost is constant at 20
Given a linear demand curve in inverse form, P = 200-2x, we know that the Marginal Revenue curve will have twice the slope of the demand curve.
Hence competitive output in terms of price and quantity is that level at which
MR=MC OR: 200 – 4x = 20
This gives use the quantities and price of a Monopolistic market:
| xm= | 45 |
| Pm = | 110 |
We can see an evolution in consumer surplus (triangle above Pm and under the demand curve), which is reduced.
The produced surplus highly increased, as it is the area determine by the equilibrium quantities (Xm), and the Price (Pm), from which we remove the costs of the quantities sold.
Consumer surplus = ((200-110) * 45)/2 = (90 * 45)/2= 2025
Producer surplus = (110-20) * 45 = 4050
- What would be the inefficiency created by the monopolist?
- What would be the outcome had two firms operated in the market?
SAMPLE ANSWER : In a competitive industry with 2 firms, we would be in a monopolistic competition.
If firms start to compete and ignore each other, this will result in the same equilibrium as depicted in (a). Both will increase their quantity and reduce price and they will not make profits above the normal.
Nevertheless, if we consider that each firm is conscient of the other, they are likely to produce less in order to have a surplus.
- Is such an outcome a form of a prisoner’s dilemma
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