Microeconomics problem on choosing an equivalent bundle

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In summary, Paul's utility function is U(P,H)=P+4H and he has a monthly income of $300. His grandmother gives him a gift certificate for $60 to Pizza Hut, where pizza costs $3 and hamburgers cost $6. In order to make Paul just as happy with cash instead of the gift certificate, his grandmother would have needed to give him an amount less than $60. After analyzing his spending habits, it is determined that Paul could have been just as happy with a different bundle of goods.
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Dostre
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Homework Statement


Hello. Thats my homework question, so any hints will be appreciated.

Paul consumes only two goods, pizza (P) and hamburgers (H), and considers them to be perfect substitutes, as shown by his utility function: (, ) = + 4. The price of pizza is $3 and the price of hamburgers is $6, and Paul’s monthly income is $300. 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 of as with the gift certificate?

Homework Equations


[itex]U(P,H)=P+4H[/itex] subject to [itex]300\leq 3P+6H[/itex]

The Attempt at a Solution


Paul can buy 20 pizzas with that gift certificate. I assume that the rest 300$ he will spend on hamburgers which cost 6$, so he will buy 50 hamburgers. When (P,H)=(20,50) the utility he gets is U(20,50)=20+4*50=220. Now, If my reasoning up to this step has been right, I need to figure out another bundle (P,H) which will get as much utility for Paul.
 
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I am no economist, but I strongly suspect that Paul's monthly allowance is irrelevant, and that you just have to concentrate on the utility that grandma's gift might bring if in cash form.
 

Related to Microeconomics problem on choosing an equivalent bundle

What is microeconomics?

Microeconomics is a branch of economics that focuses on individual economic units, such as households, firms, and markets, and how they make decisions regarding the allocation of scarce resources.

What is an equivalent bundle in microeconomics?

An equivalent bundle in microeconomics refers to a combination of goods and services that provide the same level of satisfaction or utility to an individual. This means that the individual would be equally happy or satisfied with either bundle and would be indifferent between the two.

Why is choosing an equivalent bundle important in microeconomics?

Choosing an equivalent bundle is important in microeconomics because it helps individuals make efficient decisions when faced with scarcity. By comparing different bundles and choosing the one that provides the same level of satisfaction, individuals can maximize their utility and make the most of their limited resources.

How do you determine an equivalent bundle?

An equivalent bundle can be determined by using an indifference curve, which represents all the combinations of goods and services that provide the same level of utility to an individual. The point where the indifference curve intersects with the budget constraint represents the equivalent bundle.

What factors influence an individual's choice of an equivalent bundle?

An individual's choice of an equivalent bundle is influenced by their preferences, budget, and the prices of goods and services. Changes in any of these factors can cause a shift in the equivalent bundle, as individuals seek to maximize their utility given the new circumstances.

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