9 Consider the following utility function for childcare (c) and all other goods (y). The marginal utilities are provided below: U(c,y)=30c1/2+yMUc=c1/215MUy=1 a) State the budget constraint if we are treating y as an index of all other goods b) Derive the Marshallian Demands for both childcare and all other goods c) State the consumers dual problem and derive the Hicksian Demands d) Derive the agent's Indirect Utility Function and Expenditure Function. e) Initially the consumer's income is M=100 and Pc0=5. It's election time in Canada, and suppose that the Likeable Party of Canada (LPC) promised to cap the price of childcare at Pc1=3. The policy will subsidize each unit of childcare by 2 to achieve this. Calculate the agent's total change in demand from this policy, and decompose it between the income and substitution effects using the Hicks method. f) Suppose the Congenial Party of Canada (CPC) proposed an alternative childcare policy: a cash transfer to help the agent pay childcare costs. The transfer would be the same amount as the total subsidy spent on the agent under the LPC policy. Calculate the size of this transfer, and the quantity of both goods demanded. Calculate and compare the agent's utility under both policies. g) What do you conclude about the efficiency of cash transfers vs targeted subsidies? Do you think this model accurately captures the reality of these two policies 1 ? In your answer focus on whether you think the assumptions that underpin our model are reasonable in the context of childcare