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 indierent to the bundle (x, 2x).

Suppose that Jessica's income is M = 20 and the prices of X and Y are, respectively, p x = 4 and p y = 2.

1. (a)Write the equation of Jessica's budget line. Setting the quantity of X in the horizontal axis, graph Jessica's budget line. (5 marks)
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).
3. (c)Find Jessica's optimal bundle. Draw a new graph and represent this bundle, the budget constraint, and the indifference curve containing this bundle.

(d)Suppose that the price of Y increases to py = 5. Draw a new figure including everything you had in the graph of part (c), and add Jessica's new budget line and her new optimal bundle. Find the income effect and substitution effect for Y .