Haszon- és értékgazdaságosság

Árak és jövedelmek

A fogyasztói választás elemzésének befejezéséhez egy másik típusú információra van szükség: az X és Y árai, valamint a fogyasztó számára rendelkezésre álló összeg. A következőkben feltételezzük, hogy a fogyasztó minden pénzét a rendelkezésre álló árukra költi (az árukhoz tartozó megtakarítási kötvények). Ha P _X és P _Y az X és Y áruk árai, és M jelenti a kiadásokhoz rendelkezésre álló pénzmennyiséget, akkor az a feltétel, hogy az összes pénzt elköltik, megkapja az egyenletet

vagy Y megoldása X szempontjából, (2) Ez nyilvánvalóan egyenes vonal egyenlete lejtéssel és y-metszéssel.

A költségvetési sornak vagy ársornak nevezett sor X és Y összes kombinációját reprezentálja, amelyet a fogyasztó megengedhet magának, hogy M jövedelemmel vásároljon az adott árakon.

A fogyasztó egyensúlya

A 4. ábra egyesíti ezt az ársort és az közömbösségi görbéket, lehetővé téve a fogyasztói vásárlási döntés közvetlen elemzését. A PP 'sor a fenti (2) egyenletnek megfelelő árvonal. Az R vonal bármely pontja X és Y kombinációját képviseli, amelyet egy adott fogyasztó megfizethet; azonban R nem optimális választás. Ez látható az R és S összehasonlításával ugyanazon az ársoron. Mivel S magasabb közömbösségi görbén fekszik, mint R, az előbbi az előnyben részesített helyzet, és mivel S legfeljebb R költségekkel jár (ugyanazon az ársoron vannak, tehát mindegyik M dollárba kerül), S többet ad a fogyasztónak pénz. T azonban az árvonal és az közömbösségi görbe közötti érzékenység pontján érik el a fogyasztó legmagasabb közömbösségi görbéjét; ezért ez az optimális pont neki,figyelembe véve ízlésmintáját, a közömbösségi görbék alakjai alapján. Ez a választási probléma megoldása - elvben magyarázza a fogyasztó vásárlási döntését az általa megadott preferenciák alapján, és nem feltételezi a mérhetõ hasznossági fokot.

The tangency at the solution point has a significant interpretation. It was noted above that the slope of the indifference curve is the ratio of the marginal utilities of the two commodities. It follows that, at the optimal point T, a dollar of expenditure must offer the same utility whether spent on X or on Y. If this is not so—as at point R in Figure 4, where the consumer gets more for his money by spending a dollar on Y rather than on X—it will pay him to reallocate his expenditures between the two commodities accordingly, moving toward S from R.

Changes in prices and incomes

The diagram becomes more illuminating when one investigates how the consumer’s decision is affected by a change in his income or in the price of a commodity. Equation (2) indicates that a change in income, M, does not affect the slope of the price line, only its intercept. Thus, as the person’s income increases, the price line undergoes a sequence of parallel shifts (Figure 5). For each such line there will be a point of tangency, T, with an indifference curve, showing the consumer’s optimal bundle of purchases with the corresponding income. The locus of these points (T₁, T₂, T₃…) may be called the income–consumption curve; it shows how the consumer’s purchases vary with his income. Normally the curve will have a positive slope, as EE′ does in Figure 5A, meaning that as a person grows wealthier he will buy more of each commodity. But the slope can be negative for some stretches (GG′ in Figure 5B). In that case, X is said to be an inferior good of which the consumer buys less as his income rises.

The diagram can also be used to show what happens as the price of X varies. From equation (2) it can be seen that the Y-intercept is not affected by an increase in the price of X but that the slope of the price line grows. Thus, as P_X rises, the price line shifts from PP′ to PR′ in Figure 6. This means that, as P_X rises, M dollars will buy as much of good Y as before (the position of point P at which all M dollars are spent on commodity Y does not change), but that M dollars will now buy less of good X, so that the position of point P′ must move toward the left. Once again, by following the points of tangency between indifference curves and the price lines for various values of P_X, one contains a locus UU′, τηε price–consumption curve, showing how the consumer’s purchases vary with P_X.

Income and substitution effects

It is useful to divide the effects of the price change conceptually into two parts. An increase in the price of X obviously affects the relative cost of X and Y. But it also decreases the consumer’s overall purchasing power. The effect on purchases of this reduction of purchasing power is called the income effect of the price change. Its effect via the relative price change is called the substitution effect. The division can be carried out graphically as follows: let the price of X increase so that the price line in Figure 7 moves from PP′ to PR′, and assume an imaginary intermediate price line, LL′, with the slope of PR′ but tangent to the indifference curve that was attained with the old price line PP′. The imaginary price line has the following properties: (1) it involves the same real income as PP′ (tangency points T and S are the same indifference curve), and (2) it involves the same relative prices as the new price line since their slopes are the same. The rise in price has, in the figure, caused the demand for X to fall from C to A (the quantities of X corresponding to tangency points T and U). It has been possible to divide the total effect, CA, into two parts, the income effect, BA, and the substitution effect, CB. This breakdown is important, because a number of interesting and important theorems can be proved about the substitution effect. Two of these theorems will illustrate the point.

Under the normal assumptions of demand theory it can be proved that a rise in the price of X must, via the substitution effect, work to reduce the demand for X; the second theorem states the surprising result that, considering only substitution effects, a dollar rise in the price of X must change the demand for Y by precisely the same amount as a dollar rise in the price of Y changes the demand for X. Similar relationships have been shown to hold when there are more than two commodities involved.