a) Draw the Edgeworth box (without indifference curves), with x1 on the horizontal axis. b) The original allocation is such that Arif has two units of x1 and 1 unit of x2. Is this Pareto Optimal? Explain why or why not. (Hint: Remember, the MRS = MUx¡/MUX2, where MU is Marginal Utility) c) Graph the set of bundles which are Pareto Superior to the original allocation.
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- Derive the relationship between the quantity of X demanded and the price of X if the consumer’s indifference map vis-à-vis X and Y has curves concave to the origin. Let X be games of golf per annum and Y all other goods. Draw the indifference map and budget constraint of: (a) an amateur who pays to play golf; (b) a professional who is paid to play golf. May we conclude that golfers turn professional because they dislike the game?Assume the budget constraint and the indifference curves are both linear. Assume the consumer is willing to tradeoff 1 of good X for 1 of good Y. If the relative price of one additional good X is giving up 1/2 of good Y, then the optimal bundle of the two goods is?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
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