4. [20POINTS] Anna consumes two goods: milk (measured in gallons) and a composite good (measured in dollars). Let xm represent the gallons of milk that Anna consumes in each month and let x represent her consumption on the composite good, where its price is $1 in each month. Anna's preferences over consumption bundles (xm, xc) are summarized by the utility function: u(xm, xc) = x 0.10.9 m C Annas monthly income is $400. Let pm denote the dollar price of a gallon of milk. (Hint: MU = 0.1x 0.909; MU = 0.901x0.1) m m (a) Suppose that pm = $1. What is Anna's optimal consumption bundle? Show your work. Illustrate your answer with a neat and clear diagram showing Anna's budget line and indifference curves. Label the points at which the budget line intersects the axes and identify the optimal bundle. (b) Suppose now that the local grocery store where Anna regularly shops decides to in- troduce a discount on milk. Specifically, for each gallon of milk that Anna buys, the grocery store reduces its price from $1 per gallon to $0.50 per gallon, up to a maximum number of 50 gallons of milk per month. If Anna buys more than 50 gallons she has to pay the regular price on every gallon beyond the 50-th. In a neat and clear diagram, graph Anna's budget line. Label the points at which the budget line intersects the axes and determine the coordinates of the kink point.