Suppose one of the consumers has Leontief preferences (i.e., views the two goods as perfect complements) and the other has a Cobb-Douglas utility function. If an allocation is Pareto optimal, then the two consumers who consume both goods_ while the budget line touches both consumers' indifference curves a. will not necessarily have the same MRS; at infinitely many points b. will not necessarily have the same MRS; at exactly one point c. will necessarily have the same MRS; at infinitely many points d. will necessarily have the same MRS; at exactly one point

Suppose one of the consumers has Leontief preferences (i.e., views the two goods as perfect complements) and the other has a Cobb-Douglas utility function. If an allocation is Pareto optimal, then the two consumers who consume both goods_ while the budget line touches both consumers' indifference curves a. will not necessarily have the same MRS; at infinitely many points b. will not necessarily have the same MRS; at exactly one point c. will necessarily have the same MRS; at infinitely many points d. will necessarily have the same MRS; at exactly one point

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.2P

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Suppose one of the consumers has Leontief preferences (i.e., views the two goods as perfect complements) and the other has a Cobb-Douglas utility function. If an allocation is Pareto optimal, then the two consumers who consume both goods_ while the budget line touches both consumers' indifference curves a. will not necessarily have the same MRS; at infinitely many points b. will not necessarily have the same MRS; at exactly one point c. will necessarily have the same MRS; at infinitely many points d. will necessarily have the same MRS; at exactly one point a. will not necessarily have the same MRS; at infinitely many points
If the preferences are concave will the consumer ever consume both ofthe goods together?
For the case of two goods, give an example of a utility function U(x1, x2) that represents the preferences of a consumer who regards the two goods as perfect complements. Next, take the transformation f(U) = U³ of the your example utility function and explain if this newly gener ated function represents the original preferences. Further, provide clear arguments supporting or rejecting the claim that "f(U(x1, x2)) must be strongly increasing in (x1, x2)."
Let's suppose that an individual prefers bundle of goods A over another bundle of goods B. Let's suppose that the individual prefers the bundle of goods C to the bundle of goods B. Then we can say the individual prefers C to A because more is better than less the individual prefers A to C because more is better than less two answers are correct no answer is correct O the individual prefers A to C; because of transitivity the individual prefers C to A because of transitivity
If an allocation is Pareto optimal and if indifference curves between the two goods have no kinks, then (Select all that applies) Group of answer choices a. two consumers who consume both goods must have the same MRS between them, but consumers may consume the goods in different ratios. b. two consumers with the same income who consume both goods must have the same MRS, but if their incomes differ, their MRSs may differ. c. any two consumers who consume both goods must consume them in the same ratio. d. for any two consumers who consume both goods, neither will prefer the other consumer’s bundle to his own. e. all consumers receive the bundle that they prefer to any other bundle the economy could produce for them.
a) Assume that an individual consumes two goods, and achieves the benetby çonsuming respectively 1 x and x units of each of the goods. Define the terms indifference curve and budget condition, and show the consumer benefit-maximizing good combination in a chart. Explain why this one the combination solves the utility maximization problem. b) Assume that the preferences of the consumer can be expressed by the utility function W),4 + X, 2 and that the price per unit x 1 is p =, the price per unit x 2 is 2 p= and that the income ( m ) is 200. Find the consumer's optimal choice in this case.
Carol has very weird preferences. She only cares about quantity. When evaluating a bundle, Carol only looks at the highest amount of a good she can consume in each bundle, regardless of whether it is of eggs or dumplings. She is indifferent between two bundles only when the largest consumption of a good within each bundle is the same across bundles. So, for instance, if a bundle offers 5 eggs and 1 dumpling she finds that bundle indifferent to a bundle offering 4 eggs and 5 dumplings. These preferences are transitive. But are they monotone? And convex?
Remy and Emile consume only cheese (x,) and strawberries (x2). Remy's preferences are described by UR = min{xf, 2x5}while Emile's preferences are described by UE = xf + x5 . Remy has 8 pieces of cheese and 1 pint of strawberries while Emile has 4 pieces of cheese and 3 pints of strawberries. (a) Draw an Edgeworth box with x, on the horizontal axis and x, on the vertical axis. Position Remy on the bottom left corner and Emile on the top right corner. Indicate the total number of units of x, and x2. Label the endowment allocation. Show Remy's and Emile's indifference curves. (b) Derive the equation of the contract curve. In your graph in (a), draw the contract curve. (c) Set x1 as the numeraire, i.e., assume p, = 1 and p2 = p. Find the competitive equilibrium. Hint: For Emile to consume at a Paretoefficient allocation, what should the prices be? (d) Redraw the Edgeworth box. Indicate the equilibrium allocation, e. Draw the equilibrium budget line.
Rahul's utility function is: U(x1, x2) = min{2x1 – x2, 2x2 – x1}. Priya's utility function is: U(x1, x2) = max{2x1 – x2, 2x2 – x1} Are both Priya and Rahul always better off if they get more of one of the goods? Carefully explain.
Anna is indifferent between bread and rolls for her sandwiches. She believes that 2 slices of bread is always just as good as 1 roll. Let bread be the x-good measured in slices and rolls be the y-good measured in number of rolls. Suppose Anna has $1 to spend on bread and rolls. a) Given our assumptions on preferences and the information above, Illustrate indifference curves that represent Anna's preferences. What is her MRS? b) If the price of a slice of bread is $.10 and the price of a roll is $.25 then what bundle will she choose? Show that her MRS is not equal to the price ratio at that bundle. Illustrate your answer in your diagram for part (a). c) If the price of a slice of bread rises to $.20 then what bundle will she choose? Show that her MRS is not equal the price ratio at that bundle. In a new diagram illustrate her best bundle. d) Briefly explain why her MRS is not equal to her best bundles in parts (b) and (c). e) Illustrate her demand curve for bread.
Suppose Ann likes both pancakes (P) and waffles (W) and is always willing to substitute two pancakes for one waffle. Write the equation for Ann's utility function. a. b. Given her preferences, what is Ann's marginal utility of an additional pancake? What is Ann's marginal utility of an additional waffle? с. With pancakes on the horizontal axis and waffles on the vertical axis, graph Ann's indifference curves for U=4 and U=8. d. What is Ann's marginal rate of substitution?
Joon has preferences over two goods only-beer and pizza, both of which he loves. His initial budget line goes through bundles A and B; he chooses A. When prices change such that he faces budget line through bundles B and D, Joon chooses B. Qpizza a f b B h g D I Qbeer We want to determine which bundles are better for Joon than bundle B and which bundles are worse. For each of the areas on the graph, labeled from (a) to (j) we can say, given the information provided, that