2. Consider a small island economy where the government is contemplating imposing a tax on bananasto raise revenue for public projects. The islanders' utility from consuming bananas (B) and coconuts(C) is given by the Cobb-Douglas utility function:U(B, C)=B°C1-awhere a = 0.3.(a) Write down the consumer's optimization problem and derive the demand functions for bananasand coconuts.(b) Suppose the initial prices are PB $2 and Pc== $4, and the consumer's income is I = $100.Calculate the initial quantities of bananas and coconuts consumed.(c) Calculate the compensating variation (CV) and equivalent variation (EV) for a tax rate of t =$0.50. Interpret your results in terms of the impact on consumer welfare.(d) Determine the tax revenue per consumer after the tax is imposed, assuming supply is perfectlyelastic so the tax falls entirely on consumers.(e) Compare the impacts on consumer welfare between a flat tax equal to the revenue found in part(d) and the per-unit tax.

Step 1: Step 2: Step 3: Step 4:

Answered: 2. Consider a small island economy…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Please refer to the following information to answer the question (in bold) below: You enjoy consuming apples (A) and oranges (O). Suppose that your utility function over both goods is given by Your marginal utility function for apples is . Your marginal utility function for oranges is U (A, O) = AO³ MUA = 0³ MUO 3A0² . Currently, the price of apples is $10/peck, the price of oranges is $5/pound, and your income is $160. Assume that apples are your horizontal axis good and oranges are your vertical axis good. = When you set up the optimal decision rule for your consumer problem, which of the following statements best describes how much you will buy of apples and oranges at your consumer equilibrium? For each peck of apples, you will buy 1/3 pounds of oranges. For each peck of apples, you will buy 1 pounds of oranges. O For each peck of apples, you will buy 3 pounds of oranges. O For each peck of apples, you will buy 6 pounds of oranges.
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1
8. Consider a general equilibrium model with two commodities. The excess demand functions for the two commodities are: E1 (2P₁)¹ (P₁+2P₂) - 1 E2 == (2P2)¹ (P₁+2P₂) - 2 (a) Is Walras' law satisfied? (b) Are the goods substitutes or complements?
Q3: Are the following utility functions quasi-linear, quasi-concave, quasi-convex, homogenous of degree 0, homogenous of degree 1? Show your working: 1) U(x,y) = min(x,y) 2) U(x,y) = (x" + yaja
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A consumer with $120 income and the utility function u(x,y) = (x^2)y where x is food and y clothing can go for shopping in one of the two stores A or B, where the prices for food and clothing are respectively pAx = 1, PAy = 80 and PBx = 8, PBy = 1. (a) If she can visit only one of the stores, which one would she go and what would be her optimal bundle there? Could she afford this very bundle at the other store? (HINT: How happy would she be if she chooses to go to store A for shopping? To store B? Which one is higher and what bundle would she buy there?) (b) If she can freely visit both stores (so that she buys each good from the store where it is sold cheaper), what would be her optimal bundle? What would she buy from each store? (c) How much money would she be willing to give up (out of her $120 budget) for the ability to visit both stores as in (b) rather than being restricted to shopping in only one store (the one she chooses in (a)? (HINT: suppose she pays $A for this privilege.…
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