laborsupply elasticity is dened as: am _ at 1;- anwnefanT] E ' EraT = where the \"bar\" above a character denotes the average level before and after the tax change. Question 3 (30 points) In class, we discussed the Feldstein {1999) opmalirrcometax problem including many laborsupply margins {x1 . . . ,1!) and tax evasion {e}. Let' s start with the consumer's prob lem: I ] max Utc,x1,...,xl,e}=cgte)Zrbj{xj] s.t. {lt} ijxje +e=c, jl jI c,x|,...,x[,e where gr] is the utilitycost of underreporting income, and IIJjH is the disutility of labor supply margin j. The consumer chmses to generate income {or perhaps make deductible expenses) along I margins, and to undeneport income e, which lowers her tax bill. She uses her net income to purchase consumption, c. (a) Please write down the indirect utility function First try to do it without looking at your notes. You'll want to make a substitution and then put stars on all the relevant items to denote that they've been chosen optimally. Remember the letter to use for the mction. (b) Please take a derivative of the indirect utility function with respect to the tax rate, re membering to ignore any effect of a change in the tax rate on xi'l', . . . ,xf, c*, and e*. 1What is the term you derived called, and why did you get this result? Now let's move on to the government's problem. The government chooses the tax rate to maximize the consumer's indirect utility subject to raising the required revenue, R, and let's assume the value to society of each dollar of revenue raised is a dollar: I mtax W[t]| =V[w[,...,w],t]+R s.t. t+ [ijxje] = R, j1 where WM is utilitarian social welfare. {c} What is the term on the left hand side of the equals sign in the government's budget