Question

In: Economics

Question 1) Charlie's utility is U(x1, x2) = 4x^1/2+x2. If the price of nuts (good 1)...

Question 1) Charlie's utility is U(x1, x2) = 4x^1/2+x2. If the price of nuts (good 1) is $1, the price of berries (good 2) is $4, and his income is $132, how many units of nuts will Charlie choose?

A. 128

B. 32

C. 67

D. 64

E. 17

Question 2) Kyle's utility function is U(A, B) = AB, where A and B are the numbers of apples and bananas, respectively, that he consumes. If Kyle is consuming 15 apples and 30 bananas, then if we put apples on the horizontal axis and bananas on the vertical axis, the slope of his indifference curve at his current consumption is

A. -2

B. -16

C. -1/2

D. -4

E. -1/4

Expert Solution

1. The correct option would be

d. 64

The utility function is given as . The budget constraint is given as or . The optimal solution is where slope of budget line is equal to slope of indifference curve.

The slope of indifference curve (in absolute terms) or MRS (marginal rate of substitution) would be as or or or . The slope of budget line (in absolute terms) would be as . The optimal combination of goods would be where or or or or or units.

The optimal amount of good 2 would be hence or or or units.

2. The correct option would be

a. -2

The utility function is . The slope of indifference curve would be as or . For B=30 and A=15, we have or .

For , we have the slope of indifference curve as or or , and for a constant utility level, we have or or .

Rahul Sunny answered 3 years ago

Burt’s utility function is U(x1, x2)= min{x1,x2}. Suppose the price of good 1 is p1, the...

Burt’s utility function is U(x1, x2)= min{x1,x2}. Suppose the price of good 1 is p1, the price of good p2, the income is y. a. Derive ordinary demand functions. b. Draw indifference curves and budget line for the case when the price of good 1 is 10, the price of good 2 is 20, the income is 1200. c. Find the optimal consumption bundle.

u(x1, x2) = min {x1/2, x2/3} if the price of good 1 is $7/unit, the price...

u(x1, x2) = min {x1/2, x2/3} if the price of good 1 is $7/unit, the price of good 2 is $4/unit and income is 114.. What is this person's optimal consumption level for good 2?

Sara’s utility function is u(x1, x2) = (x1 + 2)(x2 + 1). a. Write an equation...

Sara’s utility function is u(x1, x2) = (x1 + 2)(x2 + 1). a. Write an equation for Sara’s indifference curve that goes through the point (2,8). b. Suppose that the price of each good is 1 and that Clara has an income of 11. Draw her budget line. Can Sara achieve a utility of 36 with this budget? Why or why not? c. Evaluate the marginal rate of substitution MRS at (x1, x2) = (1, 5). Provide an economic interpretation...

Sophie's utility function is given as U = 2(x1)^(1/2) + 8(x2) where x1 and x2 represent...

Sophie's utility function is given as U = 2(x1)^(1/2) + 8(x2) where x1 and x2 represent the two goods Sophie consumes. Sophie's income is $3400 and the prices are given as x1 = $2 and x2 = $160 a) derive & represent in two separate diagrams the demand for x1 and x2 ( for any income and prices) b) If Sophie's income is increased to $6600, what is the income effect on x1? Is x2 a normal good? Justify your...

Amy has utility function u (x1, x2) = min { 2(x1)^2x2, x1*(x2)^2 }. Derive Amy's demand...

Amy has utility function u (x1, x2) = min { 2*(x1)^2*x2, x1*(x2)^2 }. Derive Amy's demand function for x1 and x2. For what values (if any) of m, p1, and p2 are the goods gross complements or gross substitutes of each other?

1. Amy's utility function is U(x1 , x2) = x1x2, where x1 and x2 are Amy's...

1. Amy's utility function is U(x1 , x2) = x1x2, where x1 and x2 are Amy's consumption of banana and apple, respectively. The price of apples is $1, the price of bananas is $2, and his income is $40. (a) Find out the Amy's optimal consumption bundle. (Note that Amy's utility function is Cobb-Douglas.) (b) If the price of apples now increases to $6 and the price of bananas stays constant, what would Amy's income have to be in order...

Bridgit’s utility function is U(x1, x2)= x1 + ln x2 x1 - stamps x2 - beer...

Bridgit’s utility function is U(x1, x2)= x1 + ln x2 x1 - stamps x2 - beer Bridgit’s budget p1 x1 + p2 x2 = m p1 – price of stamps p2 – price of beer m – Bridgit’s budget a) What is Bridgit’s demand for beer and stamps? b) Is it true that Bridgit would spend every dollar in additional income on stamps? c) What happens to demand when Bridgit’s income changes (i.e. find the income elasticity)? d) What happens...

Given the utility function U(x1, x2)= -2x1 + x2^2, (a)Find the marginal utility of both the...

Given the utility function U(x1, x2)= -2x1 + x2^2, (a)Find the marginal utility of both the goods. Explain whether preferences satisfy monotonicity in both goods. (b)Using the graph with a reference bundle A, draw the indifference curve and shade the quadrants that make the consumer worse off and better off for the given preferences.

(a) Calculate the marginal utility of x1 and x2 for the following utility function u (x1;...

(a) Calculate the marginal utility of x1 and x2 for the following utility function u (x1; x2) = x 1 x 2 (b) What must be true of and for the consumer to have a positive marginal utility for each good? (c) Does the utility function above exhibit a diminishing marginal rate of substitution? Assume that and satisfy the conditions from Part b. (Hint: A utility function exhibits a diminishing marginal rate of substitution if the derivative of the marginal...

Suppose a consumer seeks to maximize the utility function U (x1; x2) = (-1/x1)-(1/x2) ; subject...

Suppose a consumer seeks to maximize the utility function U (x1; x2) = (-1/x1)-(1/x2) ; subject to the budget constraint p1x1 + p2x2 = Y; where x1 and x2 represent the quantities of goods consumed, p1 and p2 are the prices of the two goods and Y represents the consumer's income. (a)What is the Lagrangian function for this problem? Find the consumer's demand functions, x1 and x2 . (b) Show the bordered Hessian matrix, H for this problem. What does...