Jessica consumes two goods, X and Y . The quantities of X and Y that Jessica may consume are denoted by x and y, respectively. For bundles such that 0.5x 《= y 《= 2x, Jessica’s marginal rate of substitution is 1; that is, she is willing to exchange any quantity of x by the same quantity of y (as long as 0.5x 《= y 《= 2x). However, when y < 0.5x, Jessica only cares about the quantity of Y , the more of it, the better, but increasing x leaves her in the same indifference curve: any bundle (x, y) such that y < 0.5x is indifferent to the bundle (2y, y). Finally when y > 2x, then she only cares about the quantity of X, the more of it, the better, but increasing y leaves her in the same indifference curve: any bundle (x, y) such that y > 2x is indifferent to the bundle (x, 2x). Suppose that Jessica’s income is M = 20 and the prices of X and Y are, respectively, px = 4 and py = 2. (b) In a new graph, with the quantity of X on the horizontal axis, draw the indifference curve that contains the bundle (x, y) = (6, 3) and the indifference curve that contains the bundle (x, 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 x and y, respectively. For bundles such that 0.5x 《= y 《= 2x, Jessica’s marginal rate of substitution is 1; that is, she is willing to exchange any quantity of x by the same quantity of y (as long as 0.5x 《= y 《= 2x). However, when y < 0.5x, Jessica only cares about the quantity of Y , the more of it, the better, but increasing x leaves her in the same indifference curve: any bundle (x, y) such that y < 0.5x is indifferent to the bundle (2y, y). Finally when y > 2x, then she only cares about the quantity of X, the more of it, the better, but increasing y leaves her in the same indifference curve: any bundle (x, y) such that y > 2x is indifferent to the bundle (x, 2x).
Suppose that Jessica’s income is M = 20 and the prices of X and Y are, respectively, px = 4 and py = 2.
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(b) In a new graph, with the quantity of X on the horizontal axis, draw the indifference curve that contains the bundle (x, y) = (6, 3) and the indifference curve that contains the bundle (x, y) = (2, 6).
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(c) Find Jessica’s optimal bundle. Draw a new graph and represent this bundle, the budget constraint, and the indifference curve containing this bundle.
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