Applications of Consumer Theory

Some Concepts Corner Points: One good is not being consumed at all – Optimal basket lies on the axis Composite Goods: A good that represents the collective expenditure on every other good except the commodity being considered

Some Concepts

Budget line with Rationing The budget line with rationing is given by A—B. B—C is cut off. the maximum quantity of commodity X that the consumer can purchase is B. if the consumer is consuming B units it does not mean his entire budget is expended on commodity X. He will also consume D of Y to exhaust his budget B Com X X0 D A Com Y C

Budget line with Rationing a consumer will be better off without rationing than with rationing with rationing the consumer is at equilibrium at point e consuming X0 watts of electricity with the absence of rationing the consumer would be on a higher indifference curve at point e1 consuming a greater quantity (X1) of power Since an effective rationing policy makes the consumer worse-off, he will try to circumvent the rationing mechanism. I0 I1 e e1 X0 X1 Com X Com Y B Budget line with Rationing A

BUDGET LINE WITH TAX AND SUBSIDY to discourage high level consumption of a commodity government could impose an indirect tax on the consumption above a given quantity The slope of the budget line becomes steeper after Xo due to the tax (t). The equation of the line (budget line) before and after the tax will have the slopes of –Px/Py and -- (Px+t)/Py, respectively.   Com Y X0 Com X A Budget Line with Tax on Consumption Beyond X0

BUDGET LINE WITH PAYMENT IN KIND If some quantity of commodity X is given to the consumer as payment in kind, his budget line before and after the payment is given in panels A and B Panel A is the usual budget line and B is the budget line with the payment in kind From panel B if the consumer expends all his income on commodity Y he will purchase 0A and in addition consume 0D of X for free. He could also trade off some units of Y for more quantities of X (greater than D) A D Com X B Com Y

BUDGET LINE WITH TAKE IT OR LEAVE IT SUBSIDY Government could decide to provide some kind of education free (free public school). The consumer on the other hand could go to the private school to pay the full cost of attending private school From the diagram the pre-subsidy budget line is given by the straight line AB and that of the post-subsidy is ACDB After the subsidy the consumer could consume OA of other goods and 0E of schooling (free public school) or reject the subsidy and be on a budget line DB Com Y Com X B E D C A

Excise Tax Versus Lump-Sum Tax Given a choice between a lump-sum tax and an excise tax that raises the same revenue, the consumer will choose the lump sum tax (Figure 3.8).

Excise vs. Lump-sum taxes

COUPONS AND CASH SUBSIDIES Suppose the consumer has preferences for housing and other goods as shown by the indifference curves Consider two types of programs that might be implemented to increase the consumer’s purchases of housing. Income subsidy: If the consumer receives an income subsidy of S cedes from the government, the budget line moves from KJ to EG. Housing voucher: If the gov’t gives the consumer a voucher of S cedes that can only be spent on housing, the budget line moves from KJ to KFG. he is indifferent between receiving an income subsidy of S cedis and a housing voucher worth S cedis. In either case, he will select basket B.

Optimal Choice of Housing: Subsidy & Voucher If a consumer has an income I, he will choose hA units of housing. The government could induce him to choose hB units of housing with either of the ff 2 programs: Give him an income subsidy of S cedis, moving the budget line to MN. The consumer chooses basket T. Give him a housing voucher worth V cedis that can be spent only on housing, moving the budget line to KRG. The consumer chooses basket R. Since basket T lies on a higher indifference curve than basket R, a consumer with such preferences would prefer an income subsidy of S cedis over a housing voucher worth V cedis.

Index Numbers Over time, many prices change. Are consumers better or worse off “overall” as a consequence? Index numbers give approximate answers to such questions.

Index Numbers Two basic types of indices price indices, and quantity indices Each index compares expenditures in a base period and in a current period by taking the ratio of expenditures.

Quantity Index Numbers A quantity index is a price-weighted average of quantities demanded; i.e. (p1,p2) can be base period prices (p1b,p2b) or current period prices (p1t,p2t).

Quantity Index Numbers If (p1,p2) = (p1b,p2b) then we have the Laspeyres quantity index;

Quantity Index Numbers If (p1,p2) = (p1t,p2t) then we have the Paasche quantity index;

Quantity Index Numbers How can quantity indices be used to make statements about changes in welfare?

Quantity Index Numbers If then so consumers overall were better off in the base period than they are now in the current period.

Quantity Index Numbers If then so consumers overall are better off in the current period than in the base period.

Price Index Numbers A price index is a quantity-weighted average of prices; i.e. (x1,x2) can be the base period bundle (x1b,x2b) or else the current period bundle (x1t,x2t).

Price Index Numbers If (x1,x2) = (x1b,x2b) then we have the Laspeyres price index;

Price Index Numbers If (x1,x2) = (x1t,x2t) then we have the Paasche price index;

Price Index Numbers How can price indices be used to make statements about changes in welfare? Define the expenditure ratio

Price Index Numbers If then so consumers overall are better off in the current period.

Price Index Numbers But, if then so consumers overall were better off in the base period.

Full Indexation? Changes in price indices are sometimes used to adjust wage rates or transfer payments. This is called “indexation”. “Full indexation” occurs when the wages or payments are increased at the same rate as the price index being used to measure the aggregate inflation rate.

Full Indexation? Since prices do not all increase at the same rate, relative prices change along with the “general price level”. A common proposal is to index fully Social Security payments, with the intention of preserving for the elderly the “purchasing power” of these payments.

Full Indexation? The usual price index proposed for indexation is the Paasche quantity index (the Consumers’ Price Index). What will be the consequence?

Full Indexation? Notice that this index uses current period prices to weight both base and current period consumptions.

Full Indexation? x2 Base period budget constraint Base period choice

Full Indexation? x2 x1 x2b x1b Base period budget constraint Base period choice Current period budget constraint before indexation

Full Indexation? x2 Base period budget constraint Base period choice Current period budget constraint after full indexation x2b x1 x1b

Full Indexation? x2 Base period budget constraint Base period choice Current period budget constraint after indexation x2b Current period choice after indexation x1 x1b

Full Indexation? x2 Base period budget constraint Base period choice Current period budget constraint after indexation x2b Current period choice after indexation x2t x1 x1b x1t

Full Indexation? x2 (x1t,x2t) is revealed preferred to (x1b,x2b) so full indexation makes the recipient strictly better off if relative prices change between the base and current periods. x2b x2t x1 x1b x1t

Full Indexation? So suppose a social security recipient gained by 1% per year for 20 years. Q: How large would the bias have become at the end of the period?

Full Indexation? So suppose a social security recipient gained by 1% per year for 20 years. Q: How large would the bias have become at the end of the period? A: so after 20 years social security payments would be about 22% “too large”.

REVEALED PREFERENCE

Revealed Preference Analysis Suppose we observe the demands (consumption choices) that a consumer makes for different budgets. This reveals information about the consumer’s preferences. We can use this information to ...

Revealed Preference Analysis Test the behavioral hypothesis that a consumer chooses the most preferred bundle from those available. Discover the consumer’s preference relation.

Assumptions on Preferences do not change while the choice data are gathered. are strictly convex. are monotonic. Together, convexity and monotonicity imply that the most preferred affordable bundle is unique.

Assumptions on Preferences x2 If preferences are convex and monotonic (i.e. well-behaved) then the most preferred affordable bundle is unique. x2* x1* x1

Direct Preference Revelation Suppose that the bundle x* is chosen when the bundle y is affordable. Then x* is revealed directly as preferred to y (otherwise y would have been chosen).

Direct Preference Revelation x2 The chosen bundle x* is revealed directly as preferred to the bundles y and z. x* z y x1

Direct Preference Revelation That x is revealed directly as preferred to y will be written as x y. D p

Indirect Preference Revelation Suppose x is revealed directly preferred to y, and y is revealed directly preferred to z. Then, by transitivity, x is revealed indirectly as preferred to z. Write this as x z so x y and y z x z. p I D p D p p I

Indirect Preference Revelation x2 z is not affordable when x* is chosen. x* z x1

Indirect Preference Revelation x2 x* is not affordable when y* is chosen. x* y* z x1

Indirect Preference Revelation x2 z is not affordable when x* is chosen. x* is not affordable when y* is chosen. x* y* z x1

Indirect Preference Revelation x2 z is not affordable when x* is chosen. x* is not affordable when y* is chosen. So x* and z cannot be compared directly. x* y* z x1

Indirect Preference Revelation x2 z is not affordable when x* is chosen. x* is not affordable when y* is chosen. So x* and z cannot be compared directly. x* But x*x* y* D p y* z x1

Indirect Preference Revelation x2 z is not affordable when x* is chosen. x* is not affordable when y* is chosen. So x* and z cannot be compared directly. x* But x*x* y* and y* z D p y* z D p x1

Indirect Preference Revelation x2 z is not affordable when x* is chosen. x* is not affordable when y* is chosen. So x* and z cannot be compared directly. x* But x*x* y* and y* z so x* z. D p y* z D p x1 p I