Question

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 pu = 6, and Paul's monthly income is M = 300. (a) How many pizzas and hamburgers does he consume when he maxi- mizes 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?

pls use microeconomic knowledge to solve

Answer 1

1a)

Given that 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 (PP) = 3 and

the price of hamburgers (PH) = 6, and

Paul’s monthly income (M) = 300.

Thus, Paul’s equation for budget line will be

3P + 6H = 300

Rewriting the budget equation with H on the RHS.

H = 300/6 – 3/6p

H = 50 – 1/2p

If hamburgers are on the vertical axis, the slope of the budget line will be -1/2

Note the budget line is the solid straight line in the graph below

I 60 I cat mai mum point Bli

The indifference curves are the dotted line. The indifference curve which maximizes utility is the one that is the highest, where there is a corner solution and Paul only eats hamburgers.

Paul maximises utility and optimize it with the objective function and the constraint.

Max H,P U (H,P) = P + 4H

s.t. 3P + 6H = 300

The is an example of perfect substitutes. Because both the indifference curves at the budget line are straight we will have a corner solution (i.e. Paul will choose to eat all of one good). To figure out the answer these types of problems we determine which good gives a greater “bang for the buck” by comparing:

H o 3 Muh Ph ) ပ- Ph the NIM dulap - MUP PP PP

Because the indifference curve is linear the MRS is the same for any value of and H. The “bank for buck” analysis shows us that for each dollar spent, the utility is higher from hamburgers than pizza.

So Paul will spend her money only on hamburgers, he will not eat pizza. Using the budget constraint, we know he has 300 dollars and it costs $6 for a hamburger so she can afford 50 hamburgers.

So after utility maximizing: H*= 50 and P*= 0

1b)

Paul's utility function is linear. His monthly income doesn't actually matter for this equation. We can think of this exclusively as a marginal issue. By giving Paul 60 dollars to spend on pizza, he bought 20 extra pizzas, which increased his utility by 20. To increase his utility by buying hamburgers, she would have had to give him enough cash to buy five hamburgers. Each hamburger costs six dollars.

2. It is given that government wants to raise $50 a month from Mr. Blow.

There are two options given, $1 sales tax per package of cigarettes and a lump sum tax of $50 per month.

A rational consumer will be preferring lesser taxes. If Mr. Blow is rational and also a non-smoker, he will be preferring $1 sales tax per package of cigarettes than a lump sum tax of $50 per month. Because, in the former case, he will be paying sales tax only when he buys a package of cigarettes. He will be paying $50 only when he buys 50 packages of cigarettes. But in case of lump-sum tax, he has to pay $50 per month. Thus, he will choose the first one, i.e., paying $1 per cigarette package.

If he is a regular smoker and smokes more than 50 packages of cigarettes in a month, he will be preferring a lump sum tax of $50 and he will smoke more. Otherwise he will smoke less.