Midterm_23_Fall_C (1).pdf * + X @ File | F:/Midterm_23_Fall_C%20(1).pdf Sign in . .. a MENG A |~ A | | Read aloud | Ask Copilot - + 2 of 7 | 2 | LD Q 1. Matt is deciding between buying stuff (c) with price p = 1 and leisure (L) with wage w. His utility function is U(L, c) = min {2c, 3/}. (11 points) (a) Find the demand functions for leisure (L*) and stuff (c*), then find the labor supply function I*. Does Matt work more when the wage rate rises? L'= I* = + (b) Your grandma says if the wage rate goes up, Matt will supply more labor. Explain to her, in general, why that is not necessarily true and why this distinction is important in studies of developing countries. Type here to search 56OF Clear ~ 9 8 4) 11/4/2023 1:12 AMMidterm_23_Fall_C (1).pdf * + X @ File | F:/Midterm_23_Fall_C%20(1).pdf Sign in . .. a MENG A |~ A | | Read aloud | Ask Copilot - + 8 1 3 of 7 | 2 | ED Q 2. Elon Musk and Jeff Bessos are brothers. Each gets a weekly allowance of $4. Elon's prefer- ences for Tweets (good r) and News Articles (good y) can be represented by the utility function u(x, y) = ray. Suppose that both goods are $1 per unit. (20 points) (a) Write down the Lagrangian Function for Elon's utility maximization problem. L(I, y, A) = (b) Solve for Elon's optimal consumption bundle. + (c) Suppose pr rises to $2. What is Elon's new optimal consumption point? (d) How much would his parents have to increase his allowance in order to leave him exactly as well off as he was originally? How much would his parents have to decrease his allowance in order for his utility under the old prices be equal to his utility under the new prices? Type here to search 56OF Clear ~ 9 8 4) 11/4/2023 1:12 AMMidterm_23_Fall_C (1).pdf * + X @ File | F:/Midterm_23_Fall_C%20(1).pdf Sign in . .. a MENG A |~ A | | Read aloud | Ask Copilot - + 4 of7 | 2 | ED Q (e) Jeff's preferences are represented by v(z, y) = ; In(x) + ; In(y). Answer parts (b)-(d) for Jeff. Comment. + 3. Abe and Mary both purchase corn chips and chocolate milk at their friendly neighborhood convenience store. The two friends have different tastes for corn chips and chocolate milk and they end up purchasing very different quantities of the two commodities. Nevertheless, they have the same marginal rate of substitution of chocolate milk for corn chips. Explain how this is possible. (12 points) 4. Explain the two things required for a person's preferences to be "rational"? (12 points) Type here to search 56OF Clear ~ 9 8 () 2 11/4/2023 1:13 AMMidterm_23_Fall_C (1).pdf * + X @ File | F:/Midterm_23_Fall_C%20(1).pdf Sign in . .. a MENG A |~ A | | Read aloud | Ask Copilot - + 5 of7 | 2 | 09 Q 5. Natasha enjoys Flying (F) and taking Judo (J). For every flight she buys, she gets three times as much enjoyment as a Judo class. (15 points) (a) Write down a utility function that represents Natasha's preferences, U(F, J) = (b) Given that PF = 90, py = 20 and Natasha has an income of $900, solve for Natasha's utility maximizing bundle. F*= + (c) Suppose there is now a $5 per unit tax imposed Judo classes. Find the Natasha's new optimal bundle and the tax revenue. F* =_ J'= TR =_ Type here to search 56OF Clear ~ 9 8 () 2 11/4/2023 1:13 AMMidterm_23_Fall_C (1).pdf * + X @ File | F:/Midterm_23_Fall_C%20(1).pdf Sign in . .. a MENG A |~ A | | Read aloud | Ask Copilot - + 6 of 7 | 2 | ED Q 6. Peter Parker likes Acai Bowls (A) and Beer (B). His demand function for Acai Bowls is qA = m - 20pA + 10pg, where m is his income, PA is the price of Acai Bowls, PB is the price of Beer, and qa is the quantity demanded of Acai Bowls. (16 points) (a) Are Acai Bowls and Beer substitutes or complements? Why? (b) Write separate equations for demand and inverse demand of Acai Bowls when the price of Beer is held constant at $1 and Peter's income is held constant at $90. + (c) Now suppose the market has a total of 5 people identical to Peter. Write equations for market demand and inverse market demand of Acai Bowls. (d) Find the price elasticity of market demand for Acai Bowls when PA = 1. At this point, is demand inelastic, elastic, or unit elastic? Type here to search 1 0 9 8 24 X 2 0 4 9 56OF Clear ~0 0 1) 11/4/2023 1:13 AMMidterm_23_Fall_C (1).pdf * + X @ File | F:/Midterm_23_Fall_C%20(1).pdf Sign in . .. a MENG A |~ A | | Read aloud | Ask Copilot - + 7 of 7 | 2 | LD Q 7. Mrs. Leontief always drinks each cup of coffee (C) with three spoonfuls of sugar (S). She would never consider consuming these two goods in any other proportion. Suppose that her income is $5, the price per cup of coffee is $0.35 and the price per spoonful of sugar is $0.05. (14 points) (a) Write down a utility function that represents her preferences for the two goods. Draw several of her indifference curves. + (b) Find her optimal consumption bundle. Q Type here to search 56OF Clear ~ 9 () 11/4/2023 1:13 AM