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 while the budget Pareto optimal, then the two consumers who consume both goods 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 while the budget Pareto optimal, then the two consumers who consume both goods 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

Chapter6: Demand Relationships Among Goods

Section: Chapter Questions

Problem 6.9P

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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)."
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.
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?
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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?