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Unformatted text preview: PY, x', y') - X(PX, PY, M') x' PX M PX This is the derivative form of the Slutsky equation. It says that the total effect of a price change is composed of a substitution effect (where income is adjusted to keep the bundle (x', y') feasible) and an income effect. We know from ECON 201 that the substitution effect is always negatively related to the price change and that the sign of the income effect will depend on whether the good is a normal good or an inferior good. As you can see, this is simply the form of the Slutsky equation we considered without calculus, except we have replaced the 's with derivative signs. Let's summarize what we have so far: X = Xs XM x PX PX M Let's interpret each term! X = X(PX, PY, M) - X(PX, PY, M) PX PX Meaning, the (demand with the new price) (demand with the old price) (change in the price from old to new) Our example showed that this was (16 14) = 2 1 (2) 78 XS = X(PX, PY, M) - X(PX, PY, M) PX PX
(demand with new price & compensated income) (demand with old price & income) (change in the price from old to new) Our example showed that this was (15.3 14) = 1.3 1 XM x = X(PX, PY, M) - X(PX, PY, M) X(PX, PY, M) M M - M
(demand with new price & compensated income) (demand with new price & old income) original demand of x (change in income needed to compensate) Our example showed that this was (15.3 16) 14 = 0.7. -14 Okay, now let's move on to Walrasian General Equilibrium Theory... WALRASIAN THEORY General equilibrium theory studies the interdependence among various components of an economy. Liontief presented an input-output technique that won him a Nobel Prize that was essentially a special case of general equilibrium analysis where all of the functional forms are assumed to be linear with fixed coefficients. We will consider this model, which uses matrix algebra in its formulation, later in the course. The economic theory that you have been exposed to until now has been limited to partial equilibrium analysis. Partial equilibrium analysis focuses on a single market or sector of the economy at a time whil...
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- Spring '10