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Question 1. Consider the following model of housing using a simple exchange econ- omy. Suppose there are two tradeable goods: money in, and housing h. Agents may also derive utility from a non-treatable good, their superannuation 5. All agents 1' in the economy have the utility function am, h) = ln(m) + h + ln(s,-) Note that utility is written as a function of money to and housing used it. As superannu- ation 3 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.1 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 w,- 2 (10,0). Agents 51 to 100 (Type-2 Agents) already own homes, and are endowed with my 2 (5, 2). Throughout your work, 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 x,-(p, pwi) for the Type-1 agents? c) What is the Marshallian Demand function icy-(p, pwj) for the Type-2 agents? (1) 1What is the Walrassian Equilibrium in this simple exchange economy? (You should provide both the equilibrium price and consumed bundles for all agent-types.) 0) Suppose 3,; = 10 for the Type-1 agents, and s;- = 10 for the Type-2 agents. What is the utility of the two agent-types in the Walrassian Equilibrium? Suppose now that the gewernment introduces a new poliey, allowing Type-1 agents to \"access part of their superannuation\". This reduces s,- to 3.; = 5 for Type-1 agents, and increases the endowment for the Type-1 agents to L0,; : (15,0). f) What is the new Walrassian Equilibrium in this simple exchange economy? What is the utility of the two types of agents in equilibrium? How does this compare to the utility prior to the policy change? The purpose of this model was to investigate an actual government proposed policy to allow renters to access their retirement funds when buying their rst property. g) Maximum word Limit: 150 words. Describe at most three problems with this specic model as a model to investigate such a policy. For each problem, briey describe, in words, a potential change to the model to address it. [Note general comments about weaknesses of every simple exchange economy model which make no reference to the housing market will not attract marks]