Determine the market equilibrium prices and allocation.

Question 1: General Equilibrium and Welfare (50 marks)
Ann and Belle only consume cookies and milk. Ann’s utility from c cookies and m glasses of
milk is given by: uA = cA(mA)2. Belle’s preferences are represented by the utility function:
uB = (cB)2mB. Initially, their mother gives 2 cookies and 1 glass of milk to each of them, but
Ann and Belle are able to trade with each other afterwards.
a) Set Ann and Belle’s utility maximisation problems and find their Marshallian Demands.
(10 marks)
b) Determine the market equilibrium prices and allocation. Show your work. (5 marks)
c) Draw an Edgeworth box to show how trade leads to a Pareto improvement for Ann and Belle.
Label and explain your diagram. (10 marks)
d) The mother wants to maximise the social welfare function W = uA + uB. Which feasible
allocation would maximise this social welfare function? Comment on the merits and limitations
of using such a social welfare function. (10 marks)
e) The mother then decides to impose that Ann and Belle can only trade cookies and glasses
of milk at a ratio of 1:1. What would happen? Show your work and provide and discuss the
result. (10 marks)
f) Characterise the efficient ways to change the allocation. (5 marks)