Would really appreciate help on question 4 and 5 really stuck will leave a like There are N number of residents living and working in the economy. Everyone has the equal income I>0 and shares the same utility function defined over private consumption C and housing unit H as follows: U ( C, H) = GC a H1- a, where G> o is an exogenous variable (which we will explore a little further) and a e (0, 1) is a parameter. The per-unit price of consumption is denoted by p> 0 and per-unit price for housing is denoted by r> 0. 1. Set up a utility maximization problem and solve for the optimal bundle of private consumption and housing unit. 2. Derive expressions for the own-price elasticity and cross-price elasticity of demand for housing unit (i.e., H,r, H,p )- 3. What is the economic interpretation of parameter 1-a in this setup? Provide a reasonable number for this parameter and justify. 4. Now, let's assume that there is a income tax of TE (0 , 1). This means, the after-tax income for each resident is (1 - 1)1.The tax revenue is used to finance government projects (e.g, water quality control, environmental regulations, provision of parks, policing, roads, etc.). What is the total revenue? (denote this variable as G) 5. Does an increase in T always lead to an increase in G? If so, provide thoughts on whether or not this feature of the model is compatible with the reality. If not, what are some conditions under which an increase in T leads to a decrease in G?