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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3) Oğuz has the utility function U(x1,X2) = x:*x2². (X: nuts, X2: berries). %3D a) If Oğuz has 25 units of nuts and 17 units of berries, the price of nuts is 2 and the price of berries is 1 liras, what would be the optimal consumption of Oğuz? b) Assume the prices change, so that nuts cost 1 and berries cost 3 liras. What is the new demand? In this change, What is the pure substitution effect? What is the income effect? c) In the change calculated in part (b), what is the pure substitution effect? d) In the change calculated in part (b), what is the income effect? In the change calculated in part (b), what is the endowment effect?
Suppose Ed's utility from the consumption of martinis (m) is proportional to the number he drinks: U(m) = m. Further, Ed is particular about his martinis: He enjoys them in exactly three parts of gin (g) to one part vermouth (v). So we can write the utility as: U(m) = U (g, v) = min (g, 3v). (a) Provide a sketch of Ed's indifference curve in the (g, v)-space for various level of utility. (a) Let the prices be p, and p, and Ed's income be I. Find the demand functions for 9 and v [Hint: Use the proportional rule and budget constraint. No need for differential calculus] (b) Using the results in (b), what is Ed's indirect utility function? (c) Find the expenditure function; given a level of utility U, and prices pg and Pv.
If the utility function of an individual takes the form: U = U ( x 1, x2) = (x1 + 2) 2 (x2 + 3) 3 Where U is total utility, and x1 and x2 are the quantities of two commoditiies consumed: (a) Find the marginal-utility function of each of the two commodities (b) Find the value of the marginal utility of the first commodity when 3 units of each commodity are consumed.
1. Suppose you are considering to make a decent holiday dinner. In this year, to be creative, you are thinking to put Copper River Salmon from Alaska (fillet) and fresh Atlantic Lobsters from Maine as entrée on the table. Use the information given, to finish the questions below. (1) The table following provides you total utility (U) and marginal (MU) from consuming Salmon and Lobster. Suppose your total utility of Salmon consumption (U1) is a function of the units (Q as pound or lbs.) of salmon consumed, as U1 =. =/400Q. Similarly, your total utility of Lobster (U2) has the form as units (Q as lbs.) of lobster consumed, which is U2 = /36Q + 40. Now fill the empty spots in the table using the information given. Total utility and marginal utility of Salmon and Lobster. Copper River Salmon Atlantic Lobster Q (Ibs.) U1 MU1 U2 MU2 1 20.00 20.00 8.72 8.72 2 3 4. 6. 7 8 10 (2) With a certain amount of budget, you are going to purchase both Salmon and Lobsters. To maximize your total…
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.
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 2 apples, 28 oranges 3 apples, 26 oranges MUA 4 apples, 24 oranges 5 apples, 22 oranges 8 apples, 16 oranges 9 apples, 14 oranges 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. : 0³ - = Given your preferences and budget constraint, what bundle represents your consumer equilibrium for apples and oranges?
8. Let be the utility function U(x, y) =(xi + 2ya), , where x and y are the quantities consumed of two goods. (a) Show that the functional equation U(x, y) U(2,2) defines y as a function of x in a %3D neighborhood of point (2, 2). (b) If the quantity consumed of good x increases by 1 unit, by how much does the quantity have to increase or decrease? Consumed of the good and to keep utility constant? (c) If the quantity consumed of good x increases by 1%, by how much does the quantity have to increase or decrease? Consumed of the good and to keep utility constant?
Your sister’s utility function over the 2 goods X and Y is defined by: U (X,Y) = XY +4Y a. If she originally consumed 10 units of X and 24 units of Y, and if the consumption of X were increased to 12 units, how much Y would she be willing to give up and maintain the initial level of satisfaction? That is, how much less Y is needed in exchange for the increase in the consumption of X if she is to be equally satisfied before and after the change occurs? b. On a carefully constructed graph (you only need to consider X and Y values up to 50), indicate your sister’s original consumption position, with X plotted on the horizontal axis and Y on the vertical axis. Draw her indifference curve through the original consumption bundle from part a. As you can verify (or have already verified), she is indifferent to the points (10,24) and (12,21). If you double the amount of each good in these two consumption bundles, you would have the bundles (20,48) and (24,42). Since the two original bundles…
1. Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U = X2 + Y2 , derive the Marshallian demand function for good Y and evaluate the type of good. 2. Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U= X2Y2 , derive the Hicksian demand function for good Y.3. Suppose that initially PX = 2, PY = 8, I = 96 and the Marshallian demand function for good Y is given by Y∗ = (0.5I/ PY)+(0.5PX/PY)− 0.5. Calculate the own price & income elasticities of demand for good Y. Interpret your computed values and say something about the type of good.4. Suppose the economy has 100 units each of goods X and Y and the utility functions of the (only) 2 individuals are: UA (XA,YA) = X0.25Y0.75, UB (XB,YB) = X0.75Y 0.25Show that pareto-improvement is possible if,…
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 O You utility increases due to the price change U (A, 0) = AO³ You utility decreases due to the price change MUA = 0³ . 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. Let's say the price of oranges rises to $10/pound of oranges. Comparing the utility you receive from your old consumer equilibrium bundle to your new consumer equilibrium bundle, how does the increase in the price of oranges impact your level of satisfaction as a consumer? MUO = 340² ЗАО2 You utility is unaffected by the price change You utility could either rise or fall due to the price change
6.7 (1) Mary's utility function is U(b, c) = b+ 100c – c, where b is the number of silver bells in her gardem and e is the number of cockle shells. She has 500 square feet in her garden to allocate between silver bells and cockle shells. Silver bells each take up 1 square foot and cockle shells each take up 4 square feet. She gets both kinds of seeds for free. (a) To maximize her utility, given the size of her garden, Mary should plant her "budget constraint" for space. Solve the problem as if it were an ordinary demand problem.) silver bells and cockle shells. (Hint: Write down (b) If she suddenly acquires an extra 100 square feet for her garden, how much should she increase her planting of silver bells?_ How much should she increase her planting of cockle shells? (c) If Mary had only 144 square feet in her garden, how many cockle shells would she grow?- (d) If Mary grows both silver bells and cockle shells, then we know that the number of square feet in her garden must be greater…
Ayana is pitching an idea for a startup company that makes and sells solar-powered phonechargers (C). Her market research has found that consumer demand for this product can beexpressed as a function of the price of the charger itself (PC), the price of phones (PF), andthe consmer’s income (I). Consumer demand can be described by the function C(PC, PF, I) =(i−10PC)/ (PF) Suppose her chargers come in all different capacities to meet any quantity demanded, so youdon’t need to worry about restricting C to whole numbers for this problem. (a) Does this product satisfy the law of demand?Explain.

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