Homework Answers
b.
We have utility of club member: U = 28 - 2n2
To find optimal club membership, we maximize club member utility:
gives: n = 7
c.
Utility of whole club is given as:
To maximize club utility, we have:
gives: n = 28 / 3 = 9.33 or 10
d. No, the answers are different.
To maximize utility of the club, 10 members are required. 3 more members can be brought in.
Reason: At individual level, saturation occurs fast, MU declines fast but at club level, MU declines at slower rate.
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b. Suppose that the utility of a club member is U = 28n - 2n2 What...
3. Suppose your utility function (e. level of satisfaction from consuming a and b) is given...
3. Suppose your utility function (e. level of satisfaction from consuming a and b) is given by U(a, b)=a 1/32/3 where a represents apple and b represents banana. Your total income is $500. The price of apple is $5 and the price of banana is $10. (a) Write your Budget Constraint (BC). What is the Marginal Rate of Transformation? (b) Find the Marginal Rate of Substitution. (c) Find the consumption combination of bananas and apples that maximizes your utility given...
I only need answers for e and f. Problem 3: Suppose your utility function (i.e. level...
I only need answers for e and f. Problem 3: Suppose your utility function (i.e. level of satisfaction from consuming a and b) is given by ?(a, b)=?1/3?2/3 where a represents apple and b represents banana. Your total income is $500. The price of apple is $5 and the price of banana is $10.(a) Write your Budget Constraint (BC).(b) Write your Rational Choice (RC). (c) Find the consumption combination of bananas and apples that maximizes your satisfaction given your budget...
1. Dorothy's utility function is U(B, O) = (B + 2) (0 + 1) where B...
1. Dorothy's utility function is U(B, O) = (B + 2) (0 + 1) where B is her consumption of bananas and O is her consumption of oatmeal. MUB = 0 + 1, MUo = B + 2. (Place Oatmeal on the y axis.) a. Write down the expression and draw Dorothy's indifference curve through (2,8). b. Suppose po = Pb = $1 and M = $11, draw the budget constraint on the same graph as her indifference curve. c....
Suppose that a consumer’s utility function is U=xy with MUx=y and MUy=x. Suppose the consumer‘s income...
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Suppose James derives utility from two goods {x,y}, characterised by the following utility function: $u(x, y)...
Suppose James derives utility from two goods {x,y},
characterised by the following utility function: $u(x, y) =
2sqrt{x} + y$: his wealth is w = 10 let py = 1:
(a) What is his optimal basket if px = 0.50? What is her
utility?
(b) What is his optimal basket and utility if px = 0.20?
(c) Find the substitution effect and the income
effect associated with the price change.
(d) What is the change in consumer
surplus?
Suppose Linda...
Suppose Tom has a utility function U=C*L C= consumption L= hours of leisure Tom has 100...
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3. Suppose you are given the utility function: In c' 4 U=In c +- Ci and...
3. Suppose you are given the utility function: In c' 4 U=In c +- Ci and the budget constraint: C - 1+r 1+r where y = 100, y 120, and the interest rate r = 0.05. a) What is the optimal value of current consumption c*? b) What is the optimal value of future consumption, c*? c) Suppose the interest rate r -0.10. What is the new value of optimal current consumption c*? Suppose the new interest rate r =...
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3. Suppose your utility function (e. level of satisfaction from consuming a and b) is given by U(a, b)=a 1/32/3 where a represents apple and b represents banana. Your total income is $500. The price of apple is $5 and the price of banana is $10. (a) Write your Budget Constraint (BC). What is the Marginal Rate of Transformation? (b) Find the Marginal Rate of Substitution. (c) Find the consumption combination of bananas and apples that maximizes your utility given...
1. Dorothy's utility function is U(B, O) = (B + 2) (0 + 1) where B is her consumption of bananas and O is her consumption of oatmeal. MUB = 0 + 1, MUo = B + 2. (Place Oatmeal on the y axis.) a. Write down the expression and draw Dorothy's indifference curve through (2,8). b. Suppose po = Pb = $1 and M = $11, draw the budget constraint on the same graph as her indifference curve. c....
3. Suppose a consumer's utility function is given by U(A, B) In(A)+In(B). Suppose the price of each apple (A) is €6, and the price of a loaf of bread (B) Is €6 and the consumer's income is €120 ) Write down the Lagrangian for this problem and solve for the optimal consumption of apples and (ii) Report and interpret your solution for the Lagrange multiplier. bread. i) Evaluate the marginal utility of bread and the marginal utility of apples at...
Suppose James derives utility from two goods {x,y},
characterised by the following utility function: $u(x, y) =
2sqrt{x} + y$: his wealth is w = 10 let py = 1:
(a) What is his optimal basket if px = 0.50? What is her
utility?
(b) What is his optimal basket and utility if px = 0.20?
(c) Find the substitution effect and the income
effect associated with the price change.
(d) What is the change in consumer
surplus?
Suppose Linda...
3. Suppose you are given the utility function: In c' 4 U=In c +- Ci and the budget constraint: C - 1+r 1+r where y = 100, y 120, and the interest rate r = 0.05. a) What is the optimal value of current consumption c*? b) What is the optimal value of future consumption, c*? c) Suppose the interest rate r -0.10. What is the new value of optimal current consumption c*? Suppose the new interest rate r =...
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