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Problem Set 3 Solutions

Problem Set 3 Solutions - Problem Set 3 Solutions 1 If two...

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Problem Set 3 - Solutions 1. If two goods are perfect complements then a change in the price of one good without a change in wealth will not affect demand for the other good. The problem is that when the price of a good changes the effect on demand for the good is composed of a substitution effect (demand change from pure price change) and an income effect (price change affects income, which then affects demand). In order to see the substitution effect, we need to change price while holding utility constant and then see if the quantities demanded change. In the graph we start at point A with the steep budget constraint. Now Px falls and we draw a new budget constraint reflecting the same amount of Y and a larger quantity of X (dashed line). Notice the consumer has purchased more of X and Y but we don’t know if this is the substitution effect or income effect. If we draw a third budget constraint reflecting the new price scheme but tangent to the original utility curve (dotted line) we see that demand does not change. This implies there is no substitution effect and the increased demand results only from the income effect. We start at point A on indifference curve U 0 and with the steep budget constraint (dotted). The consumer chooses bundle A because the MRS < Px/Py (the ratio of marginal utilities is less than the ratio of prices). Then Px decreases and we draw two new budget lines, one tangent to the original indifference curve and the other reflecting the original wealth and new price of good X. In both cases the consumer only consumes good X (MRS > ratio of prices). The substitution effect is the quantity from the origin to C, while the income effect is from C to B. Other cases: Note that if the MRS is smaller than the price ratio before and after a change in Px, then there is no change: both the income and substitution effects are zero. If the MRS is bigger X Current BC BC utility compensated BC after price change Y M Curr M Util A B X UTILITY CURVES!
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