rene spends all of her income M on soda and chips. The price of soda is 2 per unit. Irene’s utility function is U (s, c) = 5 ln(1 + s) + ln(1 + c). Hint: throughout the question, you can assume M 》= 50 and pc 《 = 8 (these assumptions just rule out the possibility of corner solutions, but do not affect the way we solve the problem). (a) Derive Irene’s demand function for chips (as a function of her income and the price of chips). (b) Are chips an inferior good for Irene? Is the magnitude of the (total) effect of a decrease in price of chips greater or smaller than the corresponding substitution effect?
Irene spends all of her income M on soda and chips. The
U (s, c) = 5 ln(1 + s) + ln(1 + c).
Hint: throughout the question, you can assume M 》= 50 and pc 《 = 8 (these assumptions just rule out the possibility of corner solutions, but do not affect the way we solve the problem).
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(a) Derive Irene’s
demand function for chips (as a function of her income and the price of chips). -
(b) Are chips an inferior good for Irene? Is the magnitude of the (total) effect of a decrease in price of chips greater or smaller than the corresponding substitution effect?
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(c) Obtain Irene’s inverse demand function for chips when her income is M = 50. Show that this function is decreasing and convex.
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(d) Is Irene’s Engel curve upward sloping or downward sloping? Explain in detail.
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