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Intermediate Microeconomics Homework 1, Due 1/28 in class 1. Assume you go shopping at a grocery store. You have $20 to spend on some combination of...

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Intermediate Microeconomics Homework 1, Due 1/28 in class 1. Assume you go shopping at a grocery store. You have $20 to spend on some combination of two goods: • $1 per apple • $4 per gallon of milk You can’t subdivide goods or choose negative amounts. (a) Write the mathematical representation of the choice set you face. (b) On a 2-dimensional plane, show the choice set of apples vs gallons of milk and label a few of those points with the amount of money you would have left over. 2. Almost the same as problem 1: assume you shopping at a grocery store. You have $15 cash and a $5 gift certificate that can only be spent on apples. • $1 per apple • $4 per gallon of milk You can’t subdivide goods or choose negative amounts. (a) Write the mathematical representation of the choice set you face. (b) On a 2-dimensional plane, show the choice set of apples vs gallons of milk and label a few of those points with the amount of cash and gift certificate you would have left over. (c) From your graphical representation, can you explain when the $10 gift certificate is “worth less” than $10 cash and when it would be the same? 3. You need to allocate money between this year and next year. Assume you start with $100,000 and have to divide it two ways. First, you can put some into a savings account that will be available next year. Second, you can spend it this year. The interest rate on the savings account is 3%, so for each dollar you decide to save you will receive $1.03 next year. (a) Write the mathematical representation of the choice set you face. (b) On a 2-dimensional plane where the x-axis is wealth this year and the y-axis is wealth next year, draw the choice set. (c) How is this problem related to the setup of problem 1? 4. A student is about to graduate with an economics major from Wash U. Create a model (in this case, a choice set) of the decision this person will make of what to do in the following year. You don’t need to exhaustively list everything, but try to get what you think the main choices would be. 1
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5. For your answer in question 4, create a preference questionnaire that satisfies transitivity. 6. Say an individual has preferences over movies of the following form: • There are three separate criteria, length , drama , and romance . • Under the criteria length , she prefers “Star Wars” to “Clueless” to “The Godfather”. Denote this as S ´ l C ´ l G • Under the criteria drama , she prefers “The Godfather” to “Star Wars” to “Clueless”, G ´ d S ´ d C • Under the criteria romance , she prefers “Clueless” to “The Godfather” to “Star Wars”, C ´ r G ´ r S When faced with any pair of movies, she chooses the one that is supported by the highest number of criteria. E.g. The Godfather is preferred to Star Wars under both d and r and Star Wars only preferred under l , so she would choose The Godfather. (a) Show that this setup leads to a non-rational choice function. (b) Can you think of another real-life example where this multiple criteria problem might lead to non-transitivity? 2
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1.
(a) The budget constraint is defined as pAA+pMM =I, where pA is the price of apples, A is the
number of apples consumed, pM is the price of milk, M is the gallons of milk consumed and I is
the...

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