3.2 Analysis In the analysis section you must complete each of the steps detailed below. The required analysis draws on content covered in lectures 15. When completing the steps you must: 0 Type all equations using the 'lnsert Equation' function (or equivalent). 0 Show all of your working and include sufficient written description for the reader to follow your process. Note that hand draw figures and equations are not acceptable. There is no word/page limit for the analysis section. Step 1: Derive the marginal rate of substitution for a low income family. (4 marks) Step 2: Find the family's demands for acceptable housing, and for the composite good, as functions of the family's weekly income 1 and the price of housing PX. (Note: Do not substitute for family income or the price of housing at this step.) (16 marks) Step 3: What is the lowest level of income at which a low income family's consumption of acceptable housing will meet the Government's target? What level of utility does the family experience at this level of income? (Hint: Use the price PX = $210 at this step.) (10 marks) Step 4: What is the highest housing price at which a low income family's consumption of acceptable housing will meet the Government's target? What level of utility does the family experience at this price? (Hint: Use the income I = $600 at this step.) (10 marks) Step 5: Find a low income family's optimal consumption basket when its income is a $390 payment, plus a $210 voucher redeemable for housing. What level of utility does the family experience in this case? (Hint: Use the price P)C = $210 at this step.) (10 marks)