Chapter 16, Problem 1.1P

(Optimal Provision of Public Goods) Using at least two individual consumers, show how the market demand curve is derived from individual demand curves (a) for a private good and (b) for a public good. Once you have derived the market demand curve in each case, introduce a market supply curve and then show the optimal level of production.

To determine

the market demand curve is to be derived from individual demand curves for a private goods and for a public good and then introduce the market supply curve and show the optimal level of production.

Concept Introduction:

A demand curve is a graph that shows the change in quantity demanded of a good or service with respect to its price. With change in price the demand also change and it carries an inverse relationship with the price. Market demand refers to the demand of a good in a particular market that adds up to a sum of different individual demands.

Explanation of Solution

Individual demand curves adds up to make a market demand curve for a good. It is a broader term that defines demand of a particular good at a much larger scale.

a. For a private good: Private good refers to the good that needs to be purchased from the private individual and its consumption by one individual prevents it to be consumed from the other individuals.

In the above figure there are three curves, where curve 1 is the individual demand curve for a good at price $5 and quantity 5 units. The second curve represents the individual demand curve for the same good at same price but the quantity is 2. The third curve is the market demand curve which is the summation of curve 1 of individual 1 and curve 2 of individual 2 at price $5 same as before. The market demand curve is the summation of curve 1 and curve 2 therefore the quantity for the same is 5 + 2 = 7 units.

b. For public good: A public good is a good which is provided to all the members of the society without profit, it is provided by the government, individual or an organization. The consumption of such good doesn’t affect the consumption for others.

Public good once produced is available to all people and in identical amounts. Hence the demand for the public good is the vertical summation of each individuals demand. The marginal cost here equals the marginal benefits at e where the market demand curve and the marginal cost curve are at equilibrium. The red line on the graph represent the market demand curve and the blue line defines the marginal cost curve. Dm and Da are respectively the two individual demand curves which add up vertically with quantity being constant to make the market demand curve.

The market supply curve is an upward sloping curve which shows a positive relationship between the price and the quantity supplied. The summation of the individuals producers supply makes the market supply curve.

The optimal level of production is the point where the market demand is equal to that of the market supply and that level of intersection is called the market demand.