4. (b) There are three people and two goods in an economy. The utility functions and initialbundles are given below:U, = x11X12U2 = 2x21 + x22U3 = X31X32 + X32W1 = (0,8)W2 = (2,2)W3 = (8,0)Suppose it is suggested that the three traders move to the allocation x given by:x1 = (1,2), x2 = (8,4), x3 = (1,4).i) Calculate the marginal rate of substitution for the three at the allocation x.

4. (b) There are three people and two goods in an economy. The utility functions and initial bundles are given below: U₁ = x11x12 W₁ = (0,8) U₂ = 2x21 + x22 W₂ = (2, 2) U3 = X31X32 + x32 W3 = (8,0) Suppose it is suggested that the three traders move to the allocation x given by: x₁ = (1,2), x₂ = (8,4), x3 = (1,4). i) Calculate the marginal rate of substitution for the three at the allocation x.

4. (b) There are three people and two goods in an economy. The utility functions and initial bundles are given below: U₁ = x11x12 W₁ = (0,8) U₂ = 2x21 + x22 W₂ = (2, 2) U3 = X31X32 + x32 W3 = (8,0) Suppose it is suggested that the three traders move to the allocation x given by: x₁ = (1,2), x₂ = (8,4), x3 = (1,4). i) Calculate the marginal rate of substitution for the three at the allocation x.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

3(b)Consider the following social choice problem in the setting of consumption of two goods by two consumers. The two goods are called tillip and quillip and the two consumers are called 1 and 2. Consumer 1 has utility function U; (t,g) =6+.4 In(t) + .6 In(q) (where t is the amount of tillip 1 consumes and q is the amount of quillip). Consumer 2 has utility function U; (t,q) = 8 + In (t) + In(q). The social endowment consists of 15 units of tillip and 20 units of quillip. a. Suppose that a social dictator has social welfare functional of the following form: social welfare, as afunction of (u",u") is a weighted sum with weight 2 on the lesser of u' and u' and weight 1 on the greater of the two. What will be the welfare optimum plan chosen by this social planner? b. What is the set of all feasible, Pareto efficient allocations of the consumption good for this society? %3D
2(b)There are three people and two goods in an economy. The utility functions and the initial bundles are given below: U₁ = X11 X 12 Uz = 2X zi+ X 22 W₁ = (0,8) W=(2,2) W3= (8,0) U3 = x 31 x 32+X 32 Suppose it is suggested that the three traders move to the allocation x given by x₁= (1,2), x₂= (8,4), X3= (1,4) b. Show that x makes no one worse off than the original allocation. c. Show that x is not in the core.
1. Consider the consumer problem with two goods, apples and oranges. Let x be the amount of apples and y be the amount of oranges, and let u(x, y) = 2√x + y be the utility function of the consumer. Let på be the price of apples, py be price of oranges, and I be the income of the consumer. (a) Using the condition that the MRS is equal to the relative prices, that is, Px ди/дх ди/ду Py 2 derive the demand functions of apples and oranges. (b) Even though the demand function of apples does not explicitly contain I, it is assumed that I cannot be too small. Explain why this assumption is necessary. = (c) Let I 90 and suppose that py = 6. Consider a price increase of apples from 2 to 3 that leaves the price of oranges unchanged at 6. Calculate the substitution effect and the income effect from this price change regarding the demand for apples.
There are 6 cups of espresso (x1) and 6 bars of chocolate (x2) in the house. Andrew and Eric have identical preferences, U₁ = alog(x) + (1 - a)log(x), where i = A, E and a € (0, 1). Suppose the Target allocation is ((2, 2), (4, 4)). (a) What is the relationship between UA and UE in the Target? (b) Find the ratio of equilibrium prices at the Target allocation. (c) Determine the lump-sum transfer necessary to achieve the Target if An- drew is initially endowed with (4, 1) and Eric with (2,5). Set x2 as the numeraire, i.e., assume pi 1. Under what condition would require Andrew to transfer to Eric or vice versa? Why? If a > 1/3, Andrew transfers to Eric and vice versa. = p and p2 =
(c) If the preferences are concave, will the consumer ever consume both of the goods together?
D2)
2. Consider a small island economy where the government is contemplating imposing a tax on bananas to 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-a where a = 0.3. (a) Write down the consumer's optimization problem and derive the demand functions for bananas and 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 perfectly elastic 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.
Ice cream and cakes are perfect substitutes for a child, and 2 units of ice cream is always worth 3 units of cakes (however many ice creams or cakes she might have, she would be willing to give up 2 ice creams to get 3 more cakes to keep the same utility level) . (a) Write down a utility function u(x,y) that represents the child's preferences, where x is the number of ice creams and y is the number of cakes she has. (b) If the prices are px= 8 and py =5, and she has $140 to spend on the two goods this summer, what is her optimal bundle? (c) If the price of ice creams decreases slightly, down to px = 7, what happens to her optimal bundle in this case? Did it change "slightly" compared to (b)?
Rafe is optimally choosing to consume 6 apples and 3 bananas. The prices of apples and bananas are p. = 7 and pb - 7. Which of the following utility functions over quantities of apples (a) and bananas (b) could represent Rafe's preferences? = u(a, b)-a4/5 61/5 Ou(a, b) = a¹/5 64/5 Ou(a, b)-a2/3 b1/3 Ou(a, b)-a¹/3 2/3
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.
Solution sent me 20 very fast
(a.) Consider a consumer who consumes two good- X and Y - where X is an inferior (but NOT Giffen good. Consider an initial equilibrium where with an income of 100 and individual consumes 10 units of X and 12 units of Y . Now, suppose the price of the good X increases, keeping everything else unchanged. Draw a clearly labelled diagram and indicate the range of the new equilibrium due to price change. [Note: only a clean graph is required and the information that are NOT given are NOT necessary.] (b.) A monopolist- who sells microprocessors in an entire Indian market- charges INR 1200 per unitand sells 1.213 million units in the country. The firm is a recent entry- so the economists are not sure about the demand curve for the Indian market, except that it is a linear curve. Can you comment anything about the elasticity at the equilibrium? Specifically, does the equilibrium lie in the elastic or the inelastic part of the demand curve? (c.) Consider a monopolist who serves a market given…