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Question: question consider a consumer with utility function4 income z and...

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Question: Consider a consumer with utility function4, income Z, and who faces market prices of p, and py (a) Use our optimality condition of MRSy MRTay to find the relationship between x and y which must always be satisfied by a bundle that maximizes the consumers utility (b) After incorporating the consumers budget to the problem, calculate the consumers de- mand for x and y which we will call x(P Z) and y(Py, Z), respectively, because it empha- sizes the dependence of the consumers demand for each good on the price of that good and the consumers income. (e) In what we call a comparative statics exercise, calculate2) and What is the interpretation of each of these derivatives? Are they positive or negative? Does this match your intuition for what the signs should be? (d) Which derivative informs you about whether the consumer views x as a normal or inferior good? Is r a normal or inferior good? Why? Assume px-2, Py 2, and Z 100 (e) How many units of x will the consumer purchase? Suppose p, increases to p, -4 (0 How does the consumers consumption of x change? [Hint: No need to re-calculate part (a). This is twhat the demand function x(px, Z) is for.] (g) In a large diagram, draw the budget line and consumers optimal bundle of x and y using the first pair of prices. Then draw the new budget line after the change in p, and the new optimal bundle of x and y. We call this the total effect of the price change. th) At the new price of p, 4, show on your diagram how the consumers income would have to change to return the consumer to his original (and higher) indifference curve. Illustrate how the total effect can be broken down into a substitution and income effect. Are they positive or negative? What is the intuition behind these effects? MacBook Air F3 Ooo F FS F6 F7 F8 F9
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