We calculated the amount of the 2 pound per week

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Unformatted text preview: effect on Ricky's demand for pepperoni as follows: XI = X(PX, PY, M) X(PX, PY, M) XI = X(2, PY, 120) X(2, PY, 106) XI = 16 15.3 XI = 0.7 pounds per week So we can infer that pepperoni is a normal good for Ricky, since as his income increases (we are moving from BLC to BLF) his demand for pepperoni increases. Let's put it all together now... 76 X = Xs + XI X = 1.3 + 0.7 X = 2 It is convenient to write our expression above in terms of the rate of change and also to redefine -XI = X(PX, PY, M) X(PX, PY, M) =, the relationship becomes, X = Xs XM PX PX PX (1) We can finish this formulation by noticing that the income change, M, is related to the price change, PX, as follows: M = x PX. Solving for PX... PX = M X and subbing this into equation (1) above: X = Xs XM x PX PX M (2) We will see that this is exactly the form of the Slutsky equation derived using calculus. Deriving the Slutsky Equation Consider the Slutsky definition of the substitution effect, in which income is adjusted so as to give the consumer just enough to buy the original consumption bundle. Let's denote this bundle as (x', y'). If the prices are (PX, PY), then the consumer's actual choice with the income adjustment will depend on (PX, PY) and (x', y'). Let's call this relationship the Slutsky demand function for good X and write it as XS(PX, PY, x', y'). Suppose the original demanded bundle is (x', y') at prices (P'X, P'Y) and income, M'. The Slutsky demand function tells us what the consumer would demand facing some different prices (PX, PY) and having income PXx' + PYy'. Thus the Slutsky demand function at (PX, PY, x', y') is the ordinary demand at (PX, PY) and income PXx' + PYy'. Meaning, 77 XS(PX, PY, x', y') X(PX, PY, PX x' + PY y') This equation says that the Slutsky demand at prices (PX, PY) is the amount that the consumer would demand if they had enough income to buy their original bundle of goods (x', y'). If we differentiate the identity with respect to PX, we get XS(PX, PY, x', y') X(PX, PY, M') + X(PX, PY, M') x' PX PX M Rearranging, we have... X(PX, PY, M') = XS(PX,...
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