4.1 Income and Substitution Effects
The Law of Demand is the notion that demand curves slope downward – when the price of a commodity goes up, the quantity demanded goes down, ceteris paribus.
A price increase changes the feasible set on the budget constraint diagram. When the price of one good increases, the intercept for that good changes, and the budget line pivots, from B1 to B2. As a consequence, the opportunity cost of that good increases (line B2 is steeper than line B1). In addition, the consumer is poorer in the sense that some bundles are no longer available. The net effect of a price increase is the effect on quantity demanded of the substitution effect and the income effect.
The substitution effect is the effect of a price change on the quantity demanded due exclusively to the fact that its relative price has changed. It is always negative when a price inceases.
The income effect of a price increase is the effect on quantity demanded due exclusively to the fact that the consumer’s real income has fallen.
Finding the Substitution and Income Effect
The substitution effect is found by looking at how the quantity of goods changes when the price goes up (the budget line shifts) and simultaneously income adjusted so the level of utility is the same (the new line is parallel to the pivoted budget line, but shifted to be tangent to the original indifference curve). The change from this point to the actual new equilibrium is the income effect of the change – it is the effect when income falls, but relative prices stay the same.
The Substitution and Income Effect: Normal Good
A price increase leads to both a substitution effect and an income effect. The substitution effect is the change in quantity demanded induced by the higher price while keeping the individual at his initial utility level. It is represented by the movement from e1 to ec . The income effect is the change in quantity demanded induced by the change in income, and is represented by the movement from ec to e2. Distance C on the vertical axis is known as the compensating variation of the price change.
[Image on pg. 96]
The Substitution and Income Effect: Inferior Good
When income increases, ceteris paribus, the quantity demanded of sugar goes down. Hence, the income effect of a price increase increases quantity demanded, from xc’ to x2’. Nevertheless, quantity demanded falls when price increases, because the substitution effect (from x1’ to xc’) outweighs the income effect. [Image on pg. 98]
The Substitution and Income Effect: Giffen Good
A Giffen good Is a commodity (which is always inferior) whose demand curve slopes upward.
If quantity demanded increases in response to an increase in price, then the good is not only inferior, it is a Giffen good. The huge income effect, which increases quantity demanded outweighs the substitution effect, which decreases quantity demanded. [Image on pg. 98]
The compensated response to a price change is the change in quantity demanded resulting from changing the price while simultaneously compensating the individual with income; the substitution effect.
The uncompensated response is the observed change in quantity demanded in response to a change in the price.
Observed response = Substitution effect + Income Effect
∆x/∆p=(∆x/∆p)Compensated+ Income effect
The Slutsky Equation is a decomposition of the effect of a price change on quantity demanded into a substitution effect and an income effect.
4.2 Compensating and Equivalent Variations
The compensating variation is the amount of money by which an individual would need to be compensated for a price change to remain at his initial level of utility. (e.g. After the price of sugar increases, how much money does Samson need to bring him back to his initial level of utility?) The compensating variation is the same as the vertical distance between the two parallel budget lines when computing the substitution effect.
The equivalent variation is a change in income that is equivalent in its effect on utility to a change in the price of a commodity. (e.g. Given Samson’s bundle before the price increases, how much money would you have to take away from the individual to reduce his welfare as much as the price increase does?) To find the equivalent variation, take the budget constraint associated with the initial prices (B1), and shift it in a parallel fashion until it is tangent to the new indifference curve. The vertical distance between the two curves is the equivalent variation.
Comparing the CV and EV
The compensating variation and the equivalent variation are not equal. The two measures are different because they evaluate the welfare change in terms of different sets of relative prices. The compensating variation determines how much income, given the new prices required to compensate for the price increase (The two lines being compared have the slope created by the new prices). The equivalent variation determines how much income would have to be taken away at the original prices to do equivalent damage to the consumer’s welfare as does the price change. (The two lines being compared have the orginal slope)
4.3 Applying Compensating and Equivalent Variations
Evaluating Price Subsidies
Sometimes the government provides subsidized prices, for example on housing. Using compensating and equivalent variations, it is possible to examine how the subsidy affects the budget constraints of the individual. As long as indifference curves have the usual shape, any subsidy that changes relative prices is inefficient in the sense that the value to the recipient is less than the cost to the government.
President Carter’s Gasoline Tax
An argument was made to impose a tax on gasoline and rebate the procedes back to the gasoline consumers. These methods of compensating and equivalent variations help to tell whether this plan is theoretically possible.
Because the gasoline tax raises its opportunity cost in terms of all other goods, it is in the consumer’s interest to consume less gasoline than he did initially – even after the rebate.
The tax would therefore succeed in reducing gasoline consumption (substitution effect), but it would make gasoline consumers worse off than before the tax (the rebate was less than the compensating variation of the price increase).
4.4 Consumer Surplus
The Demand Curve as a Marginal Valuation Schedule
The marginal value of consuming a unit of a commodity is the price on the associated point of the demand curve. In this case, the marginal value of the first unit is 50 cents (A), of the second unit 34 cents (B), and the third unit, 26 cents (C). These amounts correspond to areas under the demand curve A, B, and C, respectively.
When the demand curve is smooth, we can still interpret the vertical distance from the horizontal axis to the curve as the marginal value placed on the corresponding unit. The area under the curve between two levels of consumption represents the total value placed on those units of consumption.
The demand curve can be thought of as a marginal variation schedule – for each unit of consumption, it shows the value that the consumer attaches to the additional (i.e. marginal) unit.
Prices and Consumer Surplus
Consumer surplus is the difference between what a consumer is willing to pay and what she has to pay. This is also referred to as the Marshallian consumer surplus.
The consumer surplus associated with the ability to purchase as many units of a commodity as you want at the going price is the area under the demand curve and above the going place (usually a triangle).
A two-part tariff is a pricing system under which a consumer first pays a lump sum for the right to purchase a good, and then pays a price for each unit of the good actually purchased. An example is the access fee for telephone service, which indicates that the consumer surplus exceeds the fee for service.
Effect of Price Changes on Consumer Surplus
When the price of a commodity changes from p1 to p2, the area behind the demand curve and between the two prices is a dollar measure of the resulting change in welfare.
Application of Consumer Surplus: Analysis of a Trade Quota
A trade quota is a restriction on the quantity of some commodity that can be imported into the country.
According to Tarr and Morke, the quota on Japanese cars decreased the quantity purchased from 2.69 to 1.91 million, and raised the price per car from $4,573 to $4,967. As a consequence, consumer surplus fell by $908 million, of which $753 million went to Japanese producers in the form of quota rents, and which $155 million was a deadweight loss.
Deadweight loss is the pure waste induced by an increase in the price above the efficient level.
“Exact” Consumer Surplus and the Compensated Demand Curve
An exact marginal valuation schedule must eliminate the “income effects” that are embodied in the demand curve (the value that an individual puts on an additional unit of a good may depend on the amount that he has already spent on previous units of the good.)
Compensated Demand Curve
A compensated demand curve is a schedule that shows how the quantity demanded varies with the price, assuming that, as price changes, consumers are compensated with enough income to keep them at their initial utility level.
The process of creating a compensated demand curve involves repeating these steps:
1. Pivot the budget line in (for price increases) or out (for price decreases)
2. Shift the new budget line away from the origin (for price increases) or toward the origin (for price decreases) in a parallel fashion until it is just tangent to the original indifference curve.
3. Record the new point of tangency on a second graph.