Q2 For each of the following utility functions, derive the consumer's Marshallian demand functions, 21(P1, P2,...
An individual has the utility function: U(x1,x2,x3) = ln x1 + ln x2 + 0.5ln x3. The price of good x1 is p1, the price of good x2 is p2 = 1 and the price of good x3 is p3. The individual’s income is I. Derive the Marshallian demand functions (x1* , x2*, x3* ).
Q6 Deriving Demand Function Derive demand functions x1(P1, P2, m) and x2(P1, P2, m) for the consumer with the utility function U(x1, x2) = xi x2
Consider the following utility function, u(x1;x2) = min [sqrt (x1); sqrt(ax2)]; where a > 0 a)Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? Are the two consumption goods normal goods? (b)Show two different ways to derive the Hicksian demand functions. Does the Hicksian demand increase with price?
3. Consider the following utility function, u(x1;x2)=min[xa1; bxa2]; 00 (a) [15 points] Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? Are the two consumption goods normal goods? (b) [15 points] Derive the Hicksian demand functions. Does the Hicksian demand increase with price? 3. Consider the following utility function, (a) [15 points] Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? Are the two...
U(x, y) = x1ax2(1-a) a. Solve for the marshallian demands for x1 and x2, as functions of p1, p2, and m. (Hint: your solutions will be equations, not numbers). b. For x1 find the own-price elasticity and income elasticity. c. Suppose a = 0.2, m = 100, p1 = 2, and p2=8, find the quantities of x1 and x2. d. happens to these quantities when p1 doubles to $4? e. What does this say about the price consumption curve (PCC)?
U(x, y) = x1ax2(1-a) Solve for the marshallian demands for x1 and x2, as functions of p1, p2, and m. (Hint: your solutions will be equations, not numbers). For x1 find the own-price elasticity and income elasticity. Suppose a = 0.2, m = 100, p1 = 2, and p2=8, find the quantities of x1 and x2. What happens to these quantities when p1 doubles to $4? What does this say about the price consumption curve (PCC)? 2. Suppose the price...
Derive the Marshallian demand functions for Goods X, and X, by maximizing following utility-maximizing problem. What restrictions does a Cobb-Douglas lity function (preferences) impose on demand functions? Explain your answer. marks) 1/4 Maximize u = x;"/4x2 4x, + 2x, = 100 Subject to - Use the information in above to derive the consumer's indirect utility anction (value function) and then prove Roy's identity (10 marks)
The utility function is u = x1½ + x2, and the budget constraint is m = p1x1 + p2x2. Derive the optimal demand curve for good 1, x1(p1, p2), and good 2, x2(m, p1, p2). Looking at the cross price effects (∂x1/∂p2 and ∂x2/∂p1) are goods x1 and x2 substitutes or complements? Looking at income effects (∂x1/∂m and ∂x2/∂m) are goods x1 and x2 inferior, normal or neither? Assume m=100, p1=0.5 and p2=1. Using the demand function you derived in...
Robin has the utility function U ( x1 , x2)= 1/ 5 ln ( x1 )+ 4 /5 ln ( x2 ) . a) Set up the Lagrangian and derive an expression for the marginal rate of substitution and calculate the Marshallian demand for both goods. b) What will happen to Robin’s share of expenditures on good x1 if the price of good one, p1 , increases. Verify your conclusion formally!
3. Consider the following utility function, (a) 15 points] Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? Are the two consumption goods normal goods? (b) 15 points] Derive the Hicksian demand functions. Does the Hicksian demand ncrease with price