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Let income be I = 80, Px = 4, Py = 1, and utility U = xy (with marginal utility MUx = y and MUy = x). Compute the optimal consumption bundle for the consumer. Now, let the price of x fall to 1 and the income fall to 50. Otherwise, there is no change. Is the old bundle still affordable? In what way has "purchasing power" changed, if at all? Is the old bundle optimal? Illustrate the change on a graph.Now, suppose that the price of x falls to 1, but income does not change. What is the new optimal consumption bundle? Illustrate the change on a new graph.Based on your results for parts (a) and (b), what is the effect of a change in price on the consumption of the two goods if income is adjusted so that the old bundle is just affordable? What is the effect of a change in income on the consumption of the two goods if there is no accompanying change in price?
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