Question

Suppose there are only two people, Simon and Casey, who must split a fixed income of...

  1. 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.
  1. What is the optimal distribution of income if the social welfare function is additive?
  2. What is the optimal distribution of income if the social welfare function is W= IS + 8 IC?
  3. What is the optimal distribution of income if the society only values the utility of Simon? Comment on your answers.
  4. What is the optimal distribution of income if the society only values the utility of Casey? Comment on your answers.
  5. Comment on how your answers change under question (a) if MUS = 400 and MUC = 400.

Homework Answers

Answer #1

a) To maximize W, set marginal utilities equal; the constraint is  IS + IC = 100

So, 400 - 6IC = 400 - 2IS

Substituting IC = 100- IS gives us 2IS = 6(100-IS)

Therefore,  IC = $25  IS = $75

b) Society's overall welfare is the sum of the utility of each individual i.e. Simon and Casey in this case.

400 - 2IS +  400 - 6IC = IS + 8 IC

Substituting Is = 100- Icgives us 800=14 IC + 3(100- IC)

Therefore,  IC = $45.45 IS = $54.55

c) If only Simon matters, then give all the money to Simon until MUs = 0 (unless all the money in the economy is exhuasted first)

So,  400 - 2IS = 0 hence Is =$200

Comment: Giving all the money to Simon is optimal. Infact, we would like to give him upto $200.

d) If only Casey matters, then give all the money to Casey until MUC = 0 (unless all the money in the economy is exhuasted first)

So, 400 - 6IC = 0 hence, IC = $66.67

Comment: Giving any more money to Casey will make her marginal utility negative, which is not optimal. We don't care whether the remaining money is given to Simon or not.

e) MUS = MUC = 400., for all levels of income. Hence the society is indifferent among all distributions of income.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
 Suppose there are only two people, Mr. Mullinax and Ms. Fleming, who  must split a fixed...
 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...
v Suppose there are two people, Jack and Marie, who must split a fixed income of...
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...
Suppose there is a society with two people who have the following valuations of level y...
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...
Amy has income of $M and consumes only two goods: composite good y with price $1...
Amy has income of $M and consumes only two goods: composite good y with price $1 and chocolate (good x) that costs $px per unit. Her util- ity function is U(x,y) = 2xy; and marginal utilities of composite good y and chocolate are: MUy = 2x and MUx = 2y. (a) State Amy’s optimization problem. What is the objective function? What is a constraint? (b) Draw the Amy’s budget constraint. Place chocolate on the horizontal axis, and ”expenditure all other...
Chester consumes only bread (b) and cheese (c); his utility function is U(b,c) = bc. In...
Chester consumes only bread (b) and cheese (c); his utility function is U(b,c) = bc. In Chester’s town, cheese is sold in an unusual way. The more cheese you buy, the higher the price you have to pay. In particular, c units of cheese cost Chester c2 dollars. Bread is sold in the usual way (i.e., at a constant price) and the per-unit price of bread is pb > 0. Chester’s income is m dollars. (a) Write down Chester’s budget...
1. When should the government intervene in society? Once we have chosen the path of intervention...
1. When should the government intervene in society? Once we have chosen the path of intervention what options/factors need to be considered? How have opinions evolved over time? How might interventions differ between various levels of government (local/state/federal)? 2. People often call America the “Land of the Free”. Describe, with the theoretical tools we have discussed, how our market-based system contributes to that moniker. People have also contended that America is a country where some are systematically disadvantaged. Why might...
step by step solution for the below question please Flag this Question Question 11 pts What...
step by step solution for the below question please Flag this Question Question 11 pts What is the difference between positive economics and normative economics? Group of answer choices Positive economics deals with dynamic systems, while normative economics focuses on static systems. Normative economics deals with how the world actually works, whereas positive economics focuses on what people ought to do. Positive economics requires making value judgments, while normative economics relies solely on factual statements. Normative economics applies in cases...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT