Consider the following model of housing using a simple exchange economy. Suppose there are two goods: money m, and housing h. Agents may also derive utility from a non-tradeable good, their superannuations. All agents i in the economy have the utility function

ui(m, h) = ln(m) + h + ln(si)

As superannuations is not tradeable, it has not been included as a choice variable. It will never have a 'price' attached to it. It simply adds to utility if the agent has it and doesn't if they don't. Suppose further that there are 100 agents in the economy. Agents 1 to 50 (Type-1 agents) looking to buy a home, and are endowed with i = (10, 0). Agents 51 to 100 (Type-2 Agents) already own homes, and are endowed with j = (5, 2). Assume the price of money is pm = 1.

a) Why can we assume the price of money is 1 in our modelling?

b) What is the Marshallian Demand function xi(p, pi) for the Type-1 agents?

c) What is the Marshallian Demand function xj (p, pj ) for the Type-2 agents?

d) What is the Walrasian Equilibrium in this simple exchange economy? (provide both the equilibrium price and consumed bundles for all agent-types.)

e) Suppose si = 10 for the Type-1 agents, and sj = 10 for the Type-2 agents. What is the utility of the two agent-types in the Walrasian Equilibrium?