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.)
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{2x1, x1 + x2}.
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) = B2L3.
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?)
The table below shows the unit labour requirements for four goods in two countries
A and B. For our purposes we might wish to think of A as "the rest of the World" and B
as some country of interest.
ULR
A
B
Rubber chickens (hrs/chicken)
2
4
Trousers (hrs/pair)
2
2
Poison gas (hrs/kg)
4
3
Beauty products (hrs/millihelen)
3
2
In the absence of trade, wages are £4/hr in A and £8 in B.
For each good, calculate the ratio of the unit labour requirement in each country.
What are the autarky prices of each good in each country?
If the wage in A ("rest of the world") is fixed, in what direction must the wage
in B change if the two countries open to free trade, in order for both countries to have
something that they can export to the other?
What are the highest and the lowest wages that can prevail in B with free trade,
given the £4/hr wage in A?
For which of the goods can you predict with certainty (given our assumptions) the
pattern of trade, and what is it?
Suppose that a free trade equilibrium is achieved with a £4/hr wage in A and a wage
in B which is exactly at the mid-point of the range that you found on part (d). What will
be the world prices of each good, and which country will export it?
Suppose that workers in both countries work 40 hours per week, 50 weeks per year.
Calculate their annual incomes in units of each good, both in autarky and free trade.
In what sense, if any, have these workers gained from trade? Why (briefly) do workers in
B appear to have gained, even though their wages are lower due to the effects of trade?
What general lessons do you draw from this example?
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.
Describe these preferences in words. Are Brian and Gustavo altruists?
Draw a typical indifference curve for Brian.
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?