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Problem 1 Anna loves to consume waffles and coffee, however, only in a fixed proportion. Denote by (Tw, Ic) a consumption bundle consisting of Tu waffles and To cups of coffee. Prices are denoted by Pw and Pc. Anna's preferences are given by the following utility function: u(w, c) = min{3tw, Ic}. 1. (10 points) What is Anna's utility of bundles (1,3), (2,3) and (3,2)? In a diagram where waffles(Xw) is on the horizontal axis and coffee (Tc) is on the vertical axis, draw the indifference curves passing through these three points. 2. (10 points) What is the marginal rate of substitution for (Tw, Tc). Also, determine the marginal rate of substitution (MRS ) at (1,3), (2,3) and (3,2). Does Anna have diminishing MRS? Explain why. 3. (10 points) Are Anna's preferences monotonic? If yes, are they strictly monotone? Are the preferences convex? If yes, are they strictly convex? Explain why. 4. (10 points) Suppose that prices and income are unknown. Determine Anna's demand for waffles It, (Pw, Pc, m) and demand for coffee T't (Pu, Pc, m) as function of Pu, Pc and m. 5. (10 points) Let Pw = 1, Pc = 2 and m = 14. Determine the equation of the budget line and find it's slope. Also determine the optimal consumption bundle (xt, x*) for Anna