41 Q3. Suppose that the indirect utility is v (p, I) = 27p. P, (a) Use the Roy's identity to derive the Marshallian demand. (b) Use the relationship between the indirect utility and expenditure function to derive the expenditure function. (c) Use the Shephard's lemma to obtain the Hicksian demand from the expenditure function. (d) Use the relationship between Marshallian and Hicksian demand and obtain the Hicksian demand directly from the Marshallian demand by plugging in the expenditure function. Compare your answer to (c), it should be the same.

Consider a consumer with indirect utility function v(p, w) = w - B1p1 - B2p2 √P1P2 where 3₁ and 32 are nonnegative constants. (a) Find the consumer's expenditure function. (b) Find the Hicksian and Marshallian demands for Good 1. (c) Find expressions for the substitution and income effects on Good 1 associated with a marginal increase in the price of Good 2. (d) Suppose that the price of good 1 changes from pi to kp₁ where 0 < k < 1. Find the compensating variation of this price change.

B) a) Set up the Expenditure Minimization Problem (EMP) or Dual Problem and construct the Lagrangian function b) Find the Hicksian (Compansated) demand functions and and calculate the optimal quantities of goods: X₁ and X₂ c) Calculate Expenditure function d) Show that both Marshallian and Hicksian demands functions initially provide identical numerical values

1. Consider the utility function given by u (x1, x2) = x1x3, and budget constraint given by P1x1 + P2x2 = w. (a) Solve the EMP to find the Hicksian demand function, h (p, u). (b) Find the expenditure function e (p, u). (c) Recover h (p, u) from e (p, u). (d) Noting that the indirect utility function corresponding to the UMP for this form is 4w3 v (P1, P2, w): 27p1p3' demonstrate that v (.) and e (.) are inverses of each other. (e) Using only the indirect utility function above, recover the optimal consumption bundle of the UMP (i.e., Walrasian demand function). (f) Using your answer to (e), identify the substitution effect on the quantity demanded of good 1 of a change in the price of good 1. 1; and consider the Hicksian demand curve for good 1 corresponding to , and Walrasian demand curve for good 1 corresponding to w = 1. At what price and quantity for good 1 do they intersect? Which is steeper at this point of intersection? (g) Assume P2 What does that signify? (h) Using your…

Q2. Derive the Hicksian demand and the expenditure function for u (x, y) = (0.3/x + 0.7 /y).

A consumer has Hicksian demand functions h(p1 p2, ü)=a()*"ū and h(p1 P2, u)=(1 a)()"ū. Determine this consumer's expenditure function, e(p1.P2, ū). Next, invert it obtain the indirect utility function, v(p1, p2, m). Finally, use Roy's Identity to obtain the Marshallian demand function, r(p1, P2, m), and apply Slutsky's Equation to obtain P2 P2 ahi

Question Two a) Given the following indirect utility function: v(P. y) = y(p₁ + p₂) Derive the Marshallian demand function? Ensure to state the identity used to establish the demand function

For a > 0, consider a consumer whose utility function amounts to u(x1, x2) = − exp(−ax1x2). Can you take first order conditions to solve the utility maximization problem? Explain your argument. Next solve the utility maximization problem, and derive Marshallian demands and the indirect utility function. Given your calculations, state and use the duality theorem to find the expenditure function and Hicksian demand Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.

M -)a+P (- a + B (II) Consider indirect utility function U* = (- P `P, (a) Find Marshallian demand functions for X1. (b) Find Minimum Expenditure function. (c) Find Hicksian demand functions for X2

Consider the following strictly quasi-concave utility function u(q1, 42) = J91 + 2/92 Assume that p,and p2 are the respective prices of q, andq2. a) Derive Marshallian Demand functions. b) Derive Indirect utility function c) Derive expenditure function using indirect utility function d) Derive Hicksian Demand function from the cost function. e) Derive Hicksian Demand function using expenditure funciton