#### Consumers and Consumers Surplus

Consumer’s and Consumers’ Surplus:

Another use of the True Cost-of-Living Adjustments analysis is in so called cost-benefit analysis of some government financed infrastructure project (or any other government project for that matter). These projects may for example lower transportation costs which may intensify competition and thus lower the price of some goods, or simply just benefit commuters in terms of time saved. At the same time, the government must finance these projects by taxes (maybe not right away but eventually (“only death and taxes are certain”)), which will affect prices of some other goods and services. In a cost- benefit evaluation the economist could look at a single (representative) individual and try to ascertain what this individual’s willingness to pay for the project is. If this sum is higher than her share of the cost, the project is beneficial; in the eyes of this consumer at least, and should be implemented. A more ambitious economist would try to find out what the willingness to pay of all individuals are and sum these and compare this sum with the total cost of the project. In calculating individuals’ willingness to pay the economist would be helped if he knew their demand curves for goods whose prices are affected by the project.

As an example of an infrastructure project, we may consider a road-project. E.g., the town authorities contemplate an improvement of the flow of traffic through the inner city (e.g. a new tunnel). The project can be built in various sizes, the more traffic lanes there are, the faster traffic, for example. Assume that with the least costly project the average commuter’s traveling time to work is reduced by one minute, compared to the current situation, the next project reduces the time by two minutes, the third project by three minutes etc. figure shows how much the average commuter is prepared to pay for reducing the travelling time by 1 minute (the height of the first (white) rectangle), i.e., how much he values the first project. The second rectangle shows how much he is prepared to pay for an additional minute’s time reduction, etc. In general, the height of each rectangle (the width of which is equal to one minute’s reduction) shows the marginal willingness to pay, by the average consumer/commuter. The first grey rectangle shows the cost of the first project, per commuter, and the second grey rectangle shows the additional cost incurred if the second project is implemented, i.e., it shows the marginal cost of an additional minutes time reduction. Note that total cost (per commuter) of the second project is equal to the sum of the first and second grey rectangles. Now, the decision criterion is quite simple. Projects 1 to 4 all have marginal willingness’s to pay which exceeds the marginal cost; for project 5 the marginal willingness to pay (or simply the marginal benefit) is equal to the marginal cost: Project 5 should be implemented, giving the average commuter a time reduction of 5 minutes.

In this example I’ve assumed that the marginal willingness to pay for the first minute’s time reduction is the biggest and that it declines for each additional minute. This may be a reasonable assumption. It seems safe to assume that the marginal cost of each additional minute of time reduction is increasing. Road projects like the one assumed here probably only come in a few discrete alternatives, but if we instead look at some ordinary good which can be divided up into very small pieces we can approximate the total willingness to pay as an area under a (smooth) demand curve (instead of summing the rectangles). Likewise, the total cost can be expressed as an area under the marginal cost (=supply curve). Now, we’ve also taken the step from considering projects determined by the government, to study the utility that a typical consumer gets from buying a good on a market. In this case the consumer sets the marginal willingness to pay equal to the marginal cost for him personally, which is simply the price he must pay on the market. If the market for good 1 is characterized by perfect competition the total supply will be determined by the condition: p = MC. Note that this is the same as the criterion we used for determining which project size to implement, and it is the condition for the market allocation to be efficient.

In Figure given I’ve drawn a downward sloping demand curve and an upward sloping supply curve, for good 1. The market price is at the intersection of the demand and supply curves and the area under the demand curve up to the equilibrium quantity has been divided into three parts, denoted A, B and C. The whole area (A + B + C) is the gross consumer’s surplus; however, the consumer must pay C + B to the supplier and is left with only A, which is therefore the net consumer’s surplus. Note also that B is the total (variable) cost to the suppliers of good 1 and their surplus (the producers’ surplus) is equal to C. If we add the surpluses together we get the area A+C as the total surplus generated by market exchanges of good 1.

Assume now that the government intervenes on this market by imposing a tax on the supply of good 1, at the rate of t on each unit sold. This means that the (inverse) supply curve shifts up by t. The price received by the producers is now q and the price paid by the consumers is p, these prices are related as, p = q+t. What is the effect on the surpluses of this tax? Figure below gives the answer. The consumer’s (net) surplus has now shrunk, but is still denoted by A, the producers’ surplus (C) has also shrunk. Parts of these surpluses has ended up as tax revenue to the government, the grey area denoted D. However, there is a part of the loss of the total surplus which is not offset by tax revenue and that is the triangle denoted E. Economists call this part the dead weight loss of the tax. It effectively occurs because the increase in the price that consumers pay leads them to reduce their purchases of good 1 below the level at which the marginal benefit of consuming an extra unit of the good equals the marginal cost of producing it.

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