Introductory Microeconomics: Problem Set 5

Individual (or "consumer") choice.
  1. 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.

  2. Draw the indifference curve map with Good 1 on the horizontal axis, for the preferences given by       u = min{2x1x1 + 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.

  3. 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?)
    4. Now consider the more general problem when disposable income is M and the prices of books and luxuries are pB and pL. Repeat the analysis in (c) to find the demand function for books, as a function of prices and income. What special properties does this demand function have?
    5. Are these "luxuries" in the economic sense?
    6. Find the demand functions for books and luxuries when the utility function is      U(BL) = 2B1/2 + L.
      What special property arises here? Illustrate using an indifference curve diagram. Are luxuries "luxuries" in this case?

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