A consumer has utility u(x1, x2) = x1x2 for two goods. The government subsidizes half of the cost of the purchase of good 1 up to a maximum of 2 units. Thus if the consumer chooses the bundle (x1, x2), she pays p1/2 per unit up to x = 2, and p per unit thereafter. In particular, if she consumes more than two units, she receives a total subsidy of p1. Assume throughout this question that w> p. Recall that the Marshallian demand for this utility function (in the absence of any subsidy) is x(p, w) = 2w 3p1 3p2 (a) Carefully sketch the budget set. Be sure to identify relevant points of intersection with the axes. (b) Find the utility-maximizing bundle as a function of prices (P1, P2) and wealth w.