Question

(a) Put wine x on the horizontal axis and cheese y 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 efficiency? Explain. (b) Solve for the contract curve of Pareto efficient allocations in this economy and show this on your graph. (c) Find the competitive equilibrium prices and consumption for each type of consumer. Derive A's and B's demand functions (Marshallian). 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 x by A rises to 24 = 5, but is also on the contract curve. Find corresponding price of wine pı 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 pi.

Answer 1

A)

Consumer Quantity of Wine Quantity of cheese Quantity of cheese IGRI -ICA IWA Consumer A Cluantity of wine let As endowment bundle = LWA, we and is endowment bundle = ( wo wo done for your own Swami Vivekananda All the work you do is done for your own salvo

Budget constraint of A => Value of endowment of A = Value of bundle that A consumes

Budget constraint of B => Value of endowment of B = Value of bundle that B consumes

Here, IC_A and IC_B shows IC curve of A and B respectively. Yes, the initial allocation, that is, endowment bundle can be a pareto efficient allocation if the IC curve of A and B are tangent at endowment bundle but it isn't the case in the figure above.

B)

cheese TIC Ich Ich NIC Wine