3. Sheila and Bruce are going to the park. They are bringing a total of 18 ounces of chips (x) and 18 ounces of pretzels (y). Sheila and Bruce have preferences that can be represented by: US(x,y) = 3lnxs + lnys and UB(x,y) = lnxB+lny. Consider the equal division of the endowment where each receives 9 ounces of each good. a) An allocation in an exchange economy is called envy free if each individual prefers his or her own allocation of goods to the allocation received by any other individual. Is the equal division envy free? b) Is the equal division a Pareto efficient allocation of chips and pretzels? c) Given their marginal rates of substitution at the equal division allocation who values chips more highly? What will be the pattern of trade associated with every mutually beneficial trade?

3. Sheila and Bruce are going to the park. They are bringing a total of 18 ounces of chips (x) and 18 ounces of pretzels (y). Sheila and Bruce have preferences that can be represented by: US(x,y) = 3lnxs + lnys and UB(x,y) = lnxB+lny. Consider the equal division of the endowment where each receives 9 ounces of each good. a) An allocation in an exchange economy is called envy free if each individual prefers his or her own allocation of goods to the allocation received by any other individual. Is the equal division envy free? b) Is the equal division a Pareto efficient allocation of chips and pretzels? c) Given their marginal rates of substitution at the equal division allocation who values chips more highly? What will be the pattern of trade associated with every mutually beneficial trade?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.14P

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The figure below show the initial optimal point of a family who has to decide how much kids (K) to have in 5 years and at the same time how much of all other goods to consumer (measured as composite good in dollars). Now assuming that kids are inferior goods/services, show the new optimal point as e2 if the income of the family increases. IC₁ to K
3
. Show that Cobb-Douglas preferences are homothetic preferences
4. Sheila and Bruce are going backpacking. Sheila and Bruce each have 24 power bars (x) and 24 ounces of water (y). Their preferences can be represented by: U*(x°,y°) = la xS + la y and U(x",y) = 3lm x# + la y" a) Find Sheila and Bruce's MRS at endowment. Illustrate in an Edgeworth box diagram, the endowment point and the indifference curves through that point. b) What is the pattern of trade associated with mutually beneficial trades? c) Find one mutually beneficial trade where the terms of trade are 2 ounces of water (y) per 1 power bar (x). Instead of trading directly, Sheila and Bruce trade in a market. Sheila and Bruce are price takers on both the power bar and water markets. Each can buy and sell goods at the same price. Let P, be the price of a power bar and P, be the price of an ounce of water. d) Are the prices Px = 4 and Py-1 General Equilibrium prices? Briefly explain. You do NOT need to find the GE prices to answer this question. Do use the MRS at %3D endowment. e) Write…
K Illustrate the logic of the endowment effect using a kinked indifference curve. Let the angle be greater than 90 degrees. Suppose that the prices change, so the slope of the budget line through the endowment changes Use the diagram to explain why an individual whose endowment point is at the kink will only trade from the endowment point if the price change is substantial Using the line drawing tool, graph a new budget line representing a price change such that the consumer's optimal bundle is unchanged. Label this line 1² Carefully follow the instructions above, and only draw the required object Y quantity of good y X₂ X, quantity of good x a
Suppose there are two goods, co ee (C) and tea (T). The consump-tion set is R2+, so both goods can be consumed in arbitrary non-negativequantities.Abdul owns 2000 grams of co ee but does not own any tea. He hasno other wealth. The price of co ee is pC = 2 (in Dhs per gram) andthe price of tea is pT > 0 (in Dhs per gram). Abdul can sell co ee toearn income, which he can then use to buy tea or co ee. He can alsothrow co ee away (at no cost).Abdul's preferences can be represented by the utility functionu(c; t) = -(800 - c)2 - (800 - t)2;where c is the quantity of co ee (in grams) and t is the quantity of tea(in grams).(a) In separate diagrams, illustrate (i) the map of Abdul's indi erencecurves, (ii) Abdul's constraint set.(b) How much co ee and tea does Abdul decide to consume when (i)pT = 2, (ii) pT = 3, and (iii) pT = 4?(c) Illustrate Abdul's demand for co ee as a function of the price of tea (pT > 0) in an appropriate diagram.
4. Show how to construct the reference dependent utility function for two friends Kate and Mary whose gains and losses are listed as follows : Kate's net worth is $ 4.5 million ( decreased from $ 5.5 to $ 4.5 million ) Mary's net worth $ 3.2 million ( increased from $ 3 to $ 3.2 million ) ( First determine the reference point ( use a parameter ) and then derive reference utility function for each ) .
a. A consumer is willing to trade 3 units of x for 1 unitof y when she has 6 units of x and 5 units of y. She isalso willing to trade in 6 units of x for 2 units of y whenshe has 12 units of x and 3 units of y. She is indifferentbetween bundle (6, 5) and bundle (12, 3). What is theutility function for goods x and y? Hint: What is theshape of the indifference curve?b. A consumer is willing to trade 4 units of x for 1 unitof y when she is consuming bundle (8, 1). She is alsowilling to trade in 1 unit of x for 2 units of y when sheis consuming bundle (4, 4). She is indifferent betweenthese two bundles. Assuming that the utility function isCobb–Douglas of the form U (x, y) = xα y β, where α andβ are positive constants, what is the utility function forthis consumer?c. Was there a redundancy of information in part (b)? Ifyes, how much is the minimum amount of informationrequired in that question to derive the utility function?
T/F Explain Utility numbers cannot be negative since higher utility means a con- sumer is better off.
Illustrate the logic of the endowment effect using a kinked indifference curve. Let the angle be greater than 90 degrees. Suppose that the prices change, so the slope of the budget line through the endowment changes. Use the diagram to explain why an individual whose endowment point is at the kink will only trade from the endowment point if the price change is substantial. Using the line drawing tool, graph a new budget line representing a price change such that the consumer's optimal bundle is unchanged. Label this line 'L².. Carefully follow the instructions above, and only draw the required object. Consumers might stick with the bundle of goods they currently possess in response to a price change because they place a value on a good if they own it than they do if they are considering buying it. Y, quantity of good y Click the graph, choose a tool in the palette and follow the instructions to create your graph. e₁ X₁ X, quantity of good x
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