ECON 101 Tutorial: Week 4
Shane Murphy
s.murphy5@lancaster.ac.uk
Office Hours: Monday 3:00-4:00 – LUMS C86
Outline
• Roll Call
• Problems
• Discussion
Exercise 1
A consumer preferences over x and y are described
by the utility function u(x,y)=xy.
a) Draw two indifference curves. One representing
all bundles providing utility 9 and one
representing all bundles providing utility 16.
Exercise 1
The government has decided that the free market price of
tobacco is too low.
b) Let the price of good x be 10 and that of good y 10. Let the
consumer’s income be 60. Calculate the consumer’s
optimal consumption bundle and represent your solution
graphically. Determine the consumer’s utility.
At optimum, the slope of the indifference curve = slope of the
budget constraint
MRS = Px/Py
MRS = Mux/Muy = du/dx / du/dy = y/x
So we have y/x = 10/10 => x = y
Budget constraint is 10x + 10y = 60
Since x = y, we can rewrite this as 10x + 10x = 60
So x = 3, y = 3
Exercise 1
c) Redraw the graph of part b). Let income increase
to 80. Depict the effect of this change in wealth
on the graph. Calculate the new consumer’s
optimal consumption bundle. Determine the
consumer’s utility and compare with the one of
part b.
Now the bc is 10x + 10y = 80
So x = y = 4
Exercise 1
d) Redraw the graph of part b. Keep income at its
initial level 60 and let the price of good x fall to 5.
Depict on the graph this change in prices.
Calculate the new consumer’s optimal
consumption bundle. Determine the consumer’s
utility. Finally, represent the income and
substitution effects graphically. From the drawn
income and substitution effects is good x normal
or inferior?
Now y/x = 5/10 = ½
The budget constraint is 5x + 10y = 60
Solving we get x = 6, y = 3.
Chapter 5: Exercise 6
A person who consumes wine and cheese gets a rise, so his income increases
from 3000 to 4000. Use diagrams to show what happens if both wine and
cheese are normal goods. Now show what happens if cheese is an inferior
good.
1st figure shows the effect of an increase in income. The rise in income shifts
the budget constraint out from BC1 to BC2. If both wine and cheese are
normal goods, consumption of both increases. If cheese is an inferior good,
the increase in income causes the consumption of cheese to decline, as
shown in 2nd figure.
Chapter 6: Exercise 5
A consumer has income of 30000 a year and divides
this income between buying food and spending on
leisure. The price of food is 15 and of leisure is 10.
Draw the consumer’s BC and an IC to show an
optimum. Assume that the price of food rises in
three stages over the year in 10 increments while the
price of leisure stays at 10. Draw new BCs and
identify new optimums. Derive the demand curve for
food.
Chapter 6: Exercise 5
Discussion
In small groups, consider: Economic models optimize
some function with some constraint. Design a study
with a utility function and constraint where the study
is not of consumption goods with prices.
Is utility real? Can it be seen in brain scans?