nsi r a pure e ange economy w1 two goo . wine .1\" EEE 3; two con- sumers. A and B. Let Cheese be the numeraire good with price of $1. Consumer A's utility function is (filthy) = 2x+ y and B's utility function is lb' (I. y) = my. A's initial allocation is 10 units of .1: and 0 units of y. B's initial allocation is 0 units of :1: and 30 units of y. (a) Put wine a: on the horizontal axis and cheese :9 on the vertical axis. Measure goods for consumer A from the lower left and goods for consumer B from the upper right. 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. Is the initial resource allocation consistent with Pareto efciency? Explain. (b) Solve for the contract curve of Pareto efcient allocations in this economy and show this on your graph. to) Find the competitive equilibriiun prices and consumption for each type of consumer. Derive A*s and B's demand functions [Marshallianl Calculate the equilibrium price of wine assuming price of cheese is $1. Using demand for wine. show that Walras' Law holds. Show the budget constraint and indifference curves at the equilibrium. Label the equilibrium E. Show that E is on the contract curve. (d) Suppose instead. you wished to obtain the equilibrium E1. where consumption of good .1: by A rises to ch = 5. but is also on the contract curve. Find corresponding price of wine 1:11 that must hold in this instance. and show the set of possible new endowments [there will be a line that shows the complete set} that would satisfy the Second Theorem of Welfare Economics. given p1