Individual (or "consumer") choice.

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

- What is the professor's marginal rate of substitution between Colombian and Kenyan coffee? Draw a few of his indifference curves.
- 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.
- Draw the professor's demand curve for Colombian coffee.

- Draw the indifference curve map with Good 1 on the horizontal axis, for the preferences
given by
*u*= min{2*x*_{1},*x*_{1}+*x*_{2}}.

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

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

- 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*) =*B*^{2}*L*^{3}.

- 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? - The student chooses her consumption of books and luxuries to maximize her utility. Will she spend all her income? Why?
- 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?)
- Now consider the more general problem when disposable income is
*M*and the prices of books and luxuries are*p*and_{B}*p*. 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?_{L} - Are these "luxuries" in the economic sense?
- Find the demand functions for books and luxuries when the utility function is
*U*(*B*,*L*) = 2*B*^{1/2}+*L*.

What special property arises here? Illustrate using an indifference curve diagram. Are luxuries "luxuries" in this case?

- Find the marginal utilities of books and luxuries, and the MRS of luxuries for books,
as a function of

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