Introductory Microeconomics: Week 3 Problems

Individual ("consumer") choice.
  1. Download the spreadsheet from the CORE Project website here with data on the distribution of income. Pick several countries of interest to you and calculate the 90/10 ratio (i.e. the ratio of mean income in the top decile to mean income in the bottom decile of the income distribution) fo r 1980, 1990, and 2014. Present the data graphically or in a table and comment on the patterns you find. (This is Exercise 1.2 from the CORE textbook.)

  2. Professor K. can't tell the difference between Colombian and Kenyan coffee - the two taste exactly the same to him.

    1. What is the professor's marginal rate of substitution between Colombian and Kenyan coffee? Draw a few of his indifference curves.
    2. The professor has £6 to spend on coffee this week. Kenyan coffee costs £1.50 per cup and Colombian coffee costs £1 per cup. Draw his budget line on the same diagram and find his optimal consumption bundle.
    3. Draw the professor's demand curve for Colombian coffee.

  3. Draw the indifference curve map with Good 1 on the horizontal axis, for the preferences given by       u = min{2x1, x1 + x2}.

    Predict, using a diagram, this consumer's demands if

    1. the price of Good 1 is 2, the price of Good 2 is 1, and their budget is 6;
    2. the prices of both goods are 1 and their budget is 4.
    3. Show that they are equally well-off in either situation.

  4. A student receives a bursary of £2,000 per annum. £1,000 of this is needed for essential expenditure. The rest can be spent on books, priced at £20 each (with no second-hand value) and luxuries, priced at £10 (which contribute only to current utility). The student's utility function is: U(B,L) = B2L3.

    1. Find the marginal utilities of books and luxuries, and the MRS of luxuries for books, as a function of B and L. Is this a well-behaved utility function?
    2. The student chooses her consumption of books and luxuries to maximize her utility. Will she spend all her income? Why?
    3. Use the indifference curve - budget line tangency condition to find the student's optimal consumption of books and luxuries. (How do we know we are justified in using the tangency condition in this case?)

  5. Brian's utility function is UB = WB2 / WG , where WB is Brian's wealth and WG is Gustavo's wealth. Similarly Gustavo's utility is given by UG = WG2 / WB.

    1. Describe these preferences in words. Are Brian and Gustavo altruists?
    2. Draw a typical indifference curve for Brian.
    3. Suppose that initially both Brian and Gustavo have Wealth = 10. If they cooperate in producing a microeconomics course, they will be given a further 10 to share. What is the minimum payment Brian will demand to play his part in the collaboration? What about Gustavo? Will the course happen?

    This question from the Frank textbook.
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