Question

v

Suppose there are two people, Jack and Marie, who must split a fixed income of 2000. The marginal utilities of income for Jack and Marie are as follows:

MUj = 510- 3 IC

MUm = 510- 6 IN where Ij and Im are incomes of Jack and Marie respectively.

a) Draw the MU of Jack and Marie in the same Edgeworth box diagram.

b) What is the optimal distribution of income if social welfare function is additive?

c) What is the optimal distribution if society values only the utility of Jack?

Answer #1

a). The MU of Jack and Marie are drawn below :

b). If social welfare function is additive, utilities of both Jack and Marie matters equally. Therefore, the optimal distribution is at the point where both individual's MU are same.

SWF = U_{j} + U_{m}

Max SWF = U_{j} + U_{m} s.t. I_{j}
+I_{m} = 2000

Solving the above maximization constraint using the langrangian function we get the following condition for optimum distribution:

MU_{j} = MU_{m}

510 - 3 I_{j} = 510 - 6 I_{m} , where
I_{j} +I_{m} = 2000

I_{m} = 666.67

I_{j} = 1333.33

c). When society values only the utility of Jack,

SWF = min {U_{j}, U_{m}} = U_{j} s.t.
I_{j} +I_{m} = 2000

Solving the above maximization constraint using the langrangian function we get the following condition for optimum distribution:

MU_{j} = 0

510 - 3I_{j} = 0

I_{j} = 170

I_{m} = 2000 - 170 = 1830

Suppose there are only two people, Simon and Casey, who must
split a fixed income of $100. For Simon, the marginal utility of
income is MUS = 400 - 2IS, while for Casey,
marginal utility is MUC = 400 - 6IC, where
IS and IC are the amounts of income to Simon
and Casey, respectively.
What is the optimal distribution of income if the social
welfare function is additive?
What is the optimal distribution of income if the social
welfare...

Suppose there are only two people, Mr. Mullinax
and Ms. Fleming, who must split a fixed income of $50,000.
For Mr. Mullinax, the marginal utility of income falls and
for Ms. Fleming, marginal utility of income also falls. The utility
functions are identical. I(m) and I(f) are the initial
amounts of income to Mr. Mullinax and Ms. Fleming,
respectively.
a) What is the optimal distribution of income if the
social welfare function is additive? Why?
b) What is...

Suppose there are two possible income distributions in a society
of ten people. In the first distribution, nine people have incomes
of $30,000 and one person has an income of $10,000. In the second
distribution, all ten people have incomes of $25,000.
If the society had the first income distribution, the
utilitarian would argue that the marginal utility of income for the
person with an income of $10,000 is (lower/higher)
than the marginal utility of income for someone with an...

Suppose there are two possible income distributions in a society
of ten people. In the first distribution, nine people have incomes
of $30,000 and one person has an income of $10,000. In the second
distribution, all ten people have incomes of $25,000.
If the society had the first income distribution, the
utilitarian would argue that the marginal utility of income for the
person with an income of $10,000 is [lower/higher]
than the marginal utility of income for someone with an...

Suppose there is a society with two people who have the
following valuations of level y of a public good: v1(y) = 1210√y
and v2(y) = 410√y so their marginal benefits are given by 605/√y
and 205/√y, respectively. The cost of providing the public good is
given by c(y) = 10y. So we have MC(y) = 10.
Suppose that their utility is given by u1 = x1 + v1(y) and u2 =
x2 + v2(y) , where xi denotes person...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 6 minutes ago

asked 7 minutes ago

asked 8 minutes ago

asked 34 minutes ago

asked 34 minutes ago

asked 50 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago