Jenny's utility function is given below. Jenny has $12 from her job to spend. Good 1 cost some value greater than $0, good 2 cost $1, and good 3 cost $3
u(x1, x2, x3)= min(x1, x2)+ x3
a) What is Jenny's demand for good 1, x1*(p1)
b) What is Jenny's demand curve for good 1.
Jenny's utility function is given below. Jenny has $12 from her job to spend. Good 1...
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.
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* ).
The individual has a utility function of u(x1, x2) = min (4x1, 5x2) and faces prices p1=2 and p2=1. We know they consume 20 units of x2 and spend all their income. What is the demand function for x1?
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...
Anna spends all her income on wine (good 1) and cheese (good 2). Her utility function is u(x1; x2) = x1x2. Her income is m = $200. The prices for the two goods are p1 = $20 and p2 = $10 respectively. Find Annaís optimal consumption bundle. Show the complete calculations, and illustrate your answer graphically (draw the indi§erence curve and the budget constraint). How would your answer change to part (a) if Annaís utility function were given by v(x1;...
1. If a consumer has a utility function u(X1,X2) XIX: what fraction of her income will spend on good 2?
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...
Suppose a consumer has a utility function U (x1,x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given 1) Find the demand functions for x1 and x2 assuming -> 1. What is special about Р2 these demand functions? Are both goods normal? Are these tastes homothetic? <1. You probably P2 2) Now find the demand functions for x1 and x2 assuming assumed the opposite above, so now will you find something different. Explain....
1. Consider a utility-maximizing price-taking consumer in a two good world. Denote her budget constraint by p1x1 + p2x2 = w, p1,p2,w > 0,x1,x2 ≥ 0 (1) and suppose her utility function is u(x1,x2) = 2x1/2 1 + x2. (2) Since her budget set is compact and her utility function is continuous, the Extreme Value Theorem tells us there is at least one solution to this optimization problem. In fact, demand functions, xi(p1,p2,w),i = 1,2, exist for this example. (i)...
Suppose a consumer has a utility function U(x1, x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given. > 1. What is special about P2 1) Find the demand functions for and x2 assuming these demand functions? Are both goods normal? Are these tastes homothetic? 2) Now find the demand functions for x1 and x2 assuming-<1. You probably P2 assumed the opposite above, so now will you find something different. Explain 3) Graph...