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\"V r\"\"\"\"\"\"\"' OVV\"\"' 'V 0" ' \"\"\"" 6) (15 points) In this question, we introduce housing market to our simple economy. To keep things simple, assume that individuals rent houses and they can adjust their housing consumption each period. Individuals use :3 * M PC fraction of their disposable income on housing and they use (1 ac)MPC fraction on consumption of apples. The residential investment is similar to investment in capital stock: one apple invested today turns into one housing unit next period. The housing stock in the economy evolves by the formula Ht+1 = (1 6h)Ht + ItR, Where Ht is the housing stock in the economy at time t, and If is the residential investment at time t and 6;, is the depreciation rate of housing stock. Let R51 be the rental rate of housing at time t. Derive a formula for RF as a function of housing stock and other variables. What would be the effect of an increase in a: on capital stock, housing stock, residential investment, capital stock investment, savings, net exports, real exchange rate, rental rate of capital and rental rate of housing in long run and verylong run? Explain in detail by showing the changes in the relevant markets