Consider a pure exchange economy with wine (x) a cheese (y) only and two consumers only. Let cheese is numeraire good with price of $1. For each of the following set of consumers,
(i) Put wine - xon the horizontal axis and cheese - yon the vertical axis.
(ii) Measure goods for consumer Afrom the lower left and goods for consumer Bfrom the upper right.
(iii) Mark the initial allocation with the letter W. Draw the indifference curves for each person through this point. Calculate utility at this allocation for both consumers.
(iv) Define (solve for) Pareto efficient allocations and show them in your graph.
(v) Find the competitive equilibrium prices and consumptions for each type of consumer.
(vi) Verify the First Fundamental Theorem of Welfare Economics.
a) Consumer A's utility function is U(x, y) = 5x+ yand B's utility function is U(x,y) =xy. A's initial allocation is 1x and noy's. B's initial allocation is nox's and 3y's.
b) Consumer A's utility function is U(x, y) = x+ yand B's utility function is U(x, y) = min{2x,y}. Both have an initial allocation of 1 unit ofx and 1 unit ofy.