So the change in x due to the substitution effect is

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Unformatted text preview: (or penalized for a price decrease) by having enough income given back to them to purchase their old demand bundle. Of course, as I just mentioned, if the price goes down the consumer is "compensated" by having income taken away from them. Let's use an example to illustrate how we calculate the substitution effect. Suppose that Ricky has a demand function for pepperoni given by: X = 10 + __M__ 10PP 73 Originally, the government of Nova Scotia pays Ricky $120 per week in social assistance and the price of pepperoni is $3 per pound. This means that Ricky's original demand for pepperoni is 10 + 120/ (10 3) = 14 pounds per week. Now, let's suppose that the price of pepperoni falls to $2 per pound. Then his demand for pepperoni at the new price will be 10 + 120/ (10 2) = 16 pounds per week. So, as a result of the decrease in the price of pepperoni, Ricky now demands 2 pounds per week more of it. To calculate how much of this 2 pounds per week increase is due to the substitution effect, we need to calculate how much Ricky's income has to change in order to make the original consumption level of 14 pounds of pepperoni just affordable to Ricky at the new price of pepperoni ($2 per pound). M = X PP = 14 (2 3) = -14 So the level of income needed to keep Ricky's purchasing power constant is: M = M + M = 120 14 = 106 So, now we have Ricky's compensated demand for pepperoni at the new price and compensated income level. X(PX, PY, M) = X(2, PY, 106) = 10 + _106__ = 15.3 (10 2) and we can figure out how much of Ricky's demand for pepperoni changed due to the substitution effect as follows: Xs = X(PX, PY, M) - X(PX, PY, M) Xs = 15.3 14 = 1.3 pounds per week Now, we want to investigate the income effect. Remember that the income effect is the parallel shift of the budget line due to income changes once the change in the relative prices is accounted for. We simply change the consumer's income from M to M, keeping prices constant at (PX, PY). In the diagram, this is the shift from BLC to BLF and, more specifically, from B to C. 74 Y M / PY M / PY B A C Shift BLO s.e i.e Pivot BLF X BLC It is natural to call th...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.

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