Jessica consumes two goods, X and Y. The quantities of X and Y that Jessica may consume are denoted by r and y, respectively. For bundles such that 0.5r < y < 2r, lessica's marginal rate of substitution is 1; that is, she is willing to exchange any quantity of r by the same quantity of y (as long as 0.5x syS 21). However, when y < 0.5x, Jessica only cares about the quantity of Y, the more of it, the better, but increasing z leaves her in the same ndifference curve: any bundle (r, y) such that y < 0.5x is indifferent to the bundle (2y, y). Finally when y > 2r, then she only cares about the quantity of X, the more of it, the better, but increasing , leaves her in the same indifference curve: any bundle (r, y) such that y > 2r is indifferent to the bundle (x, 2r). Suppose that Jessica's income is M = 20 and the prices of X and Y are, respectively, p, = 4 and p, = 2. (a) Write the equation of Jessica's budget line. Setting the quantity of X in the horizontal axis, graph Jessica's budget line. (b) In a new graph, with the quantity of X on the horizontal axis, draw the indifference curve that contains the bundle (z, y) = (6, 3) and the indifference curve that contains the bundle (1, y) = (2, 6). (c) Find Jessica's optimal bundle. Draw a new graph and represent this bundle, the budget constraint, and the indifference curve containing this bundle.
Jessica consumes two goods, X and Y. The quantities of X and Y that Jessica may consume are denoted by r and y, respectively. For bundles such that 0.5r < y < 2r, lessica's marginal rate of substitution is 1; that is, she is willing to exchange any quantity of r by the same quantity of y (as long as 0.5x syS 21). However, when y < 0.5x, Jessica only cares about the quantity of Y, the more of it, the better, but increasing z leaves her in the same ndifference curve: any bundle (r, y) such that y < 0.5x is indifferent to the bundle (2y, y). Finally when y > 2r, then she only cares about the quantity of X, the more of it, the better, but increasing , leaves her in the same indifference curve: any bundle (r, y) such that y > 2r is indifferent to the bundle (x, 2r). Suppose that Jessica's income is M = 20 and the prices of X and Y are, respectively, p, = 4 and p, = 2. (a) Write the equation of Jessica's budget line. Setting the quantity of X in the horizontal axis, graph Jessica's budget line. (b) In a new graph, with the quantity of X on the horizontal axis, draw the indifference curve that contains the bundle (z, y) = (6, 3) and the indifference curve that contains the bundle (1, y) = (2, 6). (c) Find Jessica's optimal bundle. Draw a new graph and represent this bundle, the budget constraint, and the indifference curve containing this bundle.
Chapter10: Consumer Choice Theory
Section: Chapter Questions
Problem 8P
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