please anyone solve it, ill be your thankful.

An individual consumes two goods, food q; and clothing Q2. Their total budget is y, the prices of food and clothing are 301 and pg and their utility is 11. Suppose their preferences are represented by expenditu re fu nction Chapels) = 191192 em\"??- Assume that prioes and utilities take values such that this function has all the required properties of an expenditure function, including concavity in prices. and that consumers demand positive quantities of food and clothing. Note that v is allowed to be positive or negative. (a) Use Shephard's Lemma to show that compensated budget shares of food and clothing are 12+ uplfpg and % Uplfpg. Suppose that prices in a base period are p1 =p2 = 1. In a later period they have changed to 191 = 2, p2 = 1(2. You are asked to consider whether the overall cost of living should be regarded as having risen or fallen. {b} Explain what a true or Koniis east of living index is and show that a Koniis cost of living index evaluated at initial utility on for these preferences and these prices has the form (c) Explain what a Laspe'vr cost of living index is and show that a Laspeyra; cost of living index for these preferences and these prices has the form 4 2\" L(vn) (d) Discuss the facts that i. according to either indexI whether the cost of living has risen of fallen depends on the initial utility U.) at which it is evaluated ii. the cost of living has risen according to L(vg) but fallen according to Kwu) if initial utility is such thatU > m > %