Question

Part 2: Problems

1. Paul consumes only two goods, pizza P and hamburgers H and considers them to be perfect substitutes, as shown by his utility function U(P,H) = P+4H.The price of pizza is pP =3 and the price of hamburgers is pH =6, and Paul’s monthly income is M = 300.
   1. (a) How many pizzas and hamburgers does he consume when he maximizes utility? Is the tangency condition satisfied?

(b) Knowing that he likes pizza, Paul’s grandmother gives him a birthday gift certificate of 60 redeemable only at Pizza Hut. Though Paul is happy to get this gift, his grandmother did not realize that she could have made him exactly as happy by spending far less than she did. How much would she have needed to give him in cash to make him just as well off as with the gift certificate?

2. The government want to raise $50 a month from Mr. Blow. A $1 sales tax per package of cigarettes will raise the required revenue, as will a lump sum tax of $50 per month. Which tax would Mr. Blow prefer? Will he smoke more cigarettes under the sales tax or under the lump-sum tax?

Answer 1

A) MUp/pp=1/3=0.33{ per dollar MU from pizza}

MUh/ph=4/6=2/3=0.67{ per dollar MU from hamburger}

So he will spend all his money on hamburger.

Pizza=0

Hamburger=300/6=50

Utility=0+4*50=200

The solution is corner,so tangency condition doesn't satisfy in perfect substitues preference.

b)After giftcard

Pizza=60/3=20

Hamburger=300/6=50

Utility=20+4*50=220

Instead,if she would have given him cash . He would have spend that cash on hamburger .

To get same utility ,

Required hamburger=220/4=55

Additional hamburger=5

Additional money required=5*6=30

So Grandma could have given only 30 $ cash ,and make him better off equally.

C)The Decrease in consumer surplus with lump sum tax is equal to 50$

But Decrease in consumer surplus with 1$ per unit tax is more than 50$ as there will be deadweight loss associated with per unit tax. So CONSUMER will prefer lump sum tax.

CONSUMERs will consume more with lump sum tax as there will no effect on price of cigarettes with lumpsum tax but per unit tax will increase Equilibrium price thus lead to decrease in Quantity.