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A consumers utility function is given by U(X1, X2)=Xa1X21-a where A>0, 0<a<1 A consumer also faces the prices p1 and p2 and has income level m. Set up the expenditure minimization problem and find the expenditure function E(p,u)
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- A consumer’s utility function is given by: U(X1,X2)= X(α),X(1-α) where A>0, 0<α<1 The consumer also faces the prices P1 and P2 has income level m. a.) Obtain the consumer’s demand functions for and as well as the indirect utility function of the consumer b.) Show that the consumer’s indirect utility function is homogenous of degree zero in both prices and income. c.) Set up the expenditure minimization problem and find the expenditure function E(p,u)For each of the following utility functions, find the Marshallian demand function, the indirect utility function and the expenditure function. Assume that prices of x and x2 are p₁ and p₂ respectively and income is m. i) U(x1x2) = ln(x1+ x2) ii) U(x1x2) = (x1+ x2)For each of the following utility functions, find the Marshallian demand function, the indirect utility function and the expenditure function. Assume that prices of x1 and x2 are p1 and p2 respectively and income is m. U(x1 x2) = In (x1 + x2) U(x1 x2) = x1 + x2
- Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is px*x +y = m, which implies py = 1. Please derive the Marshallian demand function of x. Please derive the indirect utility function. Please derive the expenditure functionSuppose a consumer’s utility function is u = x_1^(3/2) x_2^(3/2) . She spends her budget of £27 for two goods. The prices of both goods are p1 = 6 and p2 = 6. Derive the Marshallian demand functions for ?1 and ?2 as functions of both prices and income. Then find the optimal consumption point for the given budget constraint.Irene spends all of her income M on soda and chips. The price of soda is 2 per unit. Irene’s utility function is U (s, c) = 5 ln(1 + s) + ln(1 + c). (a) Derive Irene’s demand function for chips (as a function of her income and the price of chips).
- A consumer's preferences are represented by the utility function If the budget constraint is P1X1 + P2X2 = M, determine the demand functions q1(P1, P2, M) and Q2(P1, P2, M). Determine also the indirect utility function V(P1,P2,M).The consumer's utility function is u(x1,x2) = x1 x2 Graph her budget constraint for P1 = 3, P2 = 2 and M = 900, and write down the equation for her budget Using the MRS= MU1/ MU2 = p11 / P2 tangency condition, find her optimal consumption bundle for these prices and income.A consumer has the following utility function:u(x) = (xρ1 + xρ2)1/ρ 1. Derive the Walrasian demand function x(p, w) and compute the indirect utility function.2. Write down the expenditure minimization program.
- An agent consumes quantity (x1,x2) of goods 1 and 2. Here is his utility function:U(x1, x2) = x13x2, his budget constraint is: p1x1+p2x2=m. 1. Show the expenditure function is homogeneous of degree 1 in pricesA consumers utility function is given by U(X1, X2)=Xa1X21-a where A>0, 0<a<1 A consumer also faces the prices p1 and p2 and has income levels. Obtain the consumers demand functions X1 and X2 as well as the indirect utility function of the consumerA consumers utility function is given by U(X1, X2)=Xa1X21-a where A>0, 0<a<1 A consumer also faces the prices p1 and p2 and has income level m. Obtain the consumers demand functions X1 and X2 as well as the indirect utility function of the consumer
