1*. Two six-year old twins, Lisa (L) and Malcolm (M), have the following initial endowments of
Cookies and Apples:
$\bar{C}_L = 5, \bar{A}_L = 5, \bar{C}_M = 5, \bar{A}_M = 5$
Let $C_L, A_L$ denote Lisa's consumption and $C_M, A_M$ denote Malcolm's consumption of
Cookies and Apples. Lisa and Malcolm have the following utility functions:
$U_L(C, A) = C \cdot A$
$U_M(C, A) = C + 2A$
a) Calculate a competitive equilibrium when Lisa and Malcolm decide to trade with each other.
b) Draw an Edgeworth diagram with Lisa in the lower-left corner and Malcolm in the upper-right
corner, where consumption of Cookies is measured on the horizontal axis and consumption of
Apples is measured on the vertical axis. Identify the initial endowments and draw the
indifference curves of Lisa and Malcolm consistent with these endowments.
c) Show graphically the Pareto dominating space given the initial endowments and show that the
competitive equilibrium is Pareto-efficient.
d) Explain the contract curve concept, and depict it graphically for Lisa and Malcolm. Explore
how different positions on the contract curve can be achieved by means of redistribution of
endowments. (Choose a different endowment point and calculate a new equilibrium. Try to find
the equation for the contract curve)
e) What are the relations among the different parts of this question and the First- and Second
Welfare Theorems?
