2. (48 points) Two consumers, two goods Consider an exchange economy with two consumers, A and B , and two goods, 1 and 2. 0 Consumer A's initial endowment is WA = (wiwi) = (6,9) and consumer B's endowment is wB = (w13,w23) = (6,3). 0 Consumer A's consumption is IA = (3311,3334) and consumer B's consumption is 1 2 133 = (3:3, 33 ). 0 Prices are p1, p2. They will be determined endogenously. Both consumers take prices as given. 0 Consumer A's utility is uA (3311,3331) = (3:114)2 Ii. Consumer B's utility is uB (x13, 1'2 ) = 2 3313(123) - a) (4 points) Write conditions on feasable allocations of 33:1, 51:}; and IE1, 3:323 given the initial endowments. (Assume consumers consume all available resources. b) (4 points) Draw an Edgeworth box representing the total resources available to both consumers and the initial endowment (note it w). Label your axes. Make it sufciently large as many other things will be drawn. c) (6 points) Find the contract curve: all the Paretooptimal allocations. Use the condi- tions on feasable allocations computed in a) to substitute $13,135 and express the curve as 1'31 as function of .31}. Draw it on yom' graph. To make sure it is drawn accurately, compute If on the curve at I); = 0, 33,14 = 4,131,,1 = 33214293114 = 8, 23h = 12. d) (6 points) Find consumer A's demands as function of his initial endowment and the prices: 33,14 (p1,p2,wh,wi1), 513,24 (p1,p2,w}4,wi). Substitute the numerical values of the initial endowment mi, mi. e) (6 points) What are consumer A's demands (rhi) if the relative prices are 1% = 1, 1% = 2, 1% = 3? Use them to represent on your graph consumer A's price-offer curve. f) (4 points) Find the formula for consumer A's priceoffer curve. Remember, it will be an equation of 17% as function of 33k (and the parameters). (Hint: use 2: to substitute 33k in the demand for 17%.) g) (4 points) The market equilibrium can be found at the intersection of A's price offer curve and the contract curve. Use your answers in c) and f) to nd the market equilibrium (rie???) Note it X\" on your graph. h) (4 points) What is the slope of A's budget constraint passing through the market equilibrium? Draw the budget constraint on your graph. i) (6 points) Find consumer B's demands 11:13 (331,192, c0113, tug ), 33%, (p1,p2,w}9,w23) and draw his price offer curve as well. j) (4 points) Draw (approximate) indifference curves of A and B passing through the market equilibrium