Consider two goods, good 1 and good 2. The consumer’s utility function is given by U(x1,x2)=V(x1)+x2....
- Consider two goods, good 1 and good 2. The consumer’s utility function is given by U(x1,x2)=V(x1)+x2.
- Derive the ordinary demand function of good 1.
- When the market price of good 1 is given P1=P1' , derive the consumer’s surplus.
- If the price is changed to P1=P1", prove that the change measured by consumer’s surplus is the same as the Compensating variation. Also prove that it is the same as Equivalent variation.
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Consider two goods, good 1 and good 2. The consumer’s utility
function is given by U(x1,x2)=V(x1)+x2....
Question-3 Suppose the consumer’s utility function is given by U (x1 , x2 ) = x1x...
Question-3 Suppose the consumer’s utility function is given by U (x1 , x2 ) = x1x 2 2 . Let the prices of good 1, good 2 be p1 , p2 , and suppose this consumer wants to reach a level of utility U (a) [2] Formulate the consumer’s problem in terms of the Lagrangian (b) [5] Derive the Hicksian demands for this consumer (c) [3] What is the expenditure for this consumer. (d) [5] Show that x H (...
Q1. Sam consumes two goods x1 and x2. Her utility function can be written as U(x1,x2)=x...
Q1. Sam consumes two goods x1 and x2. Her utility function can be written as U(x1,x2)=x 1raised to 2/3 and x 2 raised to 1/5 ⁄. Suppose the price of good x1 is P1, and the price of good x2 is P2. Sam’s income is m. [20 marks] a) [10 marks] Derive Sam’s Marshallian demand for each good. b) [5 marks] Derive her expenditure function using indirect utility function. c) [5 marks] Use part c) to calculate Hicksian demand function...
EXERCISE 2 Consider a consumer who consumes two goods and has utility function u(x1, x2) =...
EXERCISE 2 Consider a consumer who consumes two goods and has utility function u(x1, x2) = x, + 1x1 The price of good 2 is 1, the price of good 1 is p, and income is m. Derive the ordinary demand functions of good l and good 2. For what values of p and m is: a. good l normal? b. good 2 normal? c. good 1 an ordinary good? d. good 2 a gross substitute for good 1?
The utility function is u = x1½ + x2, and the budget constraint is m =...
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...
Assume that a person's utility over two goods is given by U(x1, x2) = (x1 −...
Assume that a person's utility over two goods is given by U(x1, x2) = (x1 − 10)^1/3 (x2 − 5)^2/3 The price of good x1 is equal to p1 and the price of good x2 is p2. The total income of the individual is given by I. (a) Write down the budget constraint of this person. (b) Calculate the demand for each one of the two goods. (c) Calculate the elasticity of demand for each one of the two goods.
1. Suppose that a consumer has a utility function U(x1,x2) = x0.5x0.5 . Initial prices are...
1. Suppose that a consumer has a utility function U(x1,x2) = x0.5x0.5 . Initial prices are P1=1 and P2 = 1, and income is m 100. Now, the price of good 1 increases to 2. (a) On the graph, please show initial choice (in black), new choice (in blue), compen- sating variation (in green) and equivalent variation (in red). (b) What is amount of the compensating variation? How to interpret it? (C) What is amount of the equivalent variation? How...
Robin has the utility function U ( x1 , x2)= 1/ 5 ln ( x1 )+...
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!
An individual has the utility function: U(x1,x2,x3) = ln x1 + ln x2 + 0.5ln x3....
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* ).
Suppose a consumer’s preferences over goods 1 and 2 are represented by the utility function U(x1,...
Suppose a consumer’s preferences over goods 1 and 2 are represented by the utility function U(x1, x2) = (x1 + x2) 3 . Draw an indifference curve for this consumer and indicate its slope.
There are two consumer goods, xi and x2. Consumers all have income given by m, and a utility function U(, x2) = aln(x1)...
There are two consumer goods, xi and x2. Consumers all have income given by m, and a utility function U(, x2) = aln(x1)+In(x2). The price of the two goods are pi and p2 (a) Find the individual demand functions for x1 and r2 (b) The parameter a differs across consumers. Type A consumers have a = 1. Type B consumers have a = 2. If there is one type A person and two type B people, what is market demand...
EXERCISE 2 Consider a consumer who consumes two goods and has utility function u(x1, x2) = x, + 1x1 The price of good 2 is 1, the price of good 1 is p, and income is m. Derive the ordinary demand functions of good l and good 2. For what values of p and m is: a. good l normal? b. good 2 normal? c. good 1 an ordinary good? d. good 2 a gross substitute for good 1?
1. Suppose that a consumer has a utility function U(x1,x2) = x0.5x0.5 . Initial prices are P1=1 and P2 = 1, and income is m 100. Now, the price of good 1 increases to 2. (a) On the graph, please show initial choice (in black), new choice (in blue), compen- sating variation (in green) and equivalent variation (in red). (b) What is amount of the compensating variation? How to interpret it? (C) What is amount of the equivalent variation? How...
There are two consumer goods, xi and x2. Consumers all have income given by m, and a utility function U(, x2) = aln(x1)+In(x2). The price of the two goods are pi and p2 (a) Find the individual demand functions for x1 and r2 (b) The parameter a differs across consumers. Type A consumers have a = 1. Type B consumers have a = 2. If there is one type A person and two type B people, what is market demand...
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