ASSIGNMENT 3
DUE BY 3/31 (TUESDAY)
Q1. The table below shows independent utility schedules for goods X and Y. Prices are PX = 50
and PY = 50. The consumer has income I = 250.
(a) List all possible bundles of X and Y that this consumer can afford that exactly exhaust the
budget. (Hint: the budget constraint is PX·X + PY·Y = I. Find all combinations of wholenumber quantities that satisfy this equation.)
(b) Calculate the marginal utility (MU) and marginal utility per dollar (MU/P) for each good
at each quantity.
(c) Draw the MU per dollar curves for both goods on the same diagram.
(d) Identify the optimal bundle. Verify that the budget is exhausted and that MUX/PX =
MUY/PY at the optimum.
Quantity of
X
TUₓ
Quantity of
Y
TUᵧ
1
100
1
120
2
180
2
220
3
240
3
300
4
280
4
360
5
300
5
400
Q2. Write down the budget line equation in each case. Draw both budget lines in a single
diagram.
(a) PX = 20, PY = 30, I = 120
(b) PX = 20, PY = 20, I = 120
Explain in your own words how the two budget lines differ in terms of purchasing power and
relative prices.
Q3. Write down the budget line equation in each case. Draw both budget lines in a single
diagram.
(a) PX = 20, PY = 30, I = 120
(b) PX = 20, PY = 30, I = 240
Explain in your own words how the two budget lines differ in terms of purchasing power and
relative prices.
Q4. Suppose PX = 10, PY = 10 and I = 200. Draw the budget line and label the following
bundles. For each bundle, state whether it is optimal or not and provide an explanation.
Quantity of
X
Quantity of
Y
MUₓ
MUᵧ
15
5
5
15
8
10
10
12
12
8
8
12
10
10
10
10
Q5. Suppose PX = 10, PY = 20 and I = 600. Draw the budget line and label the following
bundles. For each bundle, state whether it is optimal or not and provide an explanation.
Quantity of X
Quantity of Y
MRS
20
20
3
30
15
0.5
40
10
0.25
Q6. Consider the diagram below showing a budget line and three indifference curves (IC1, IC2,
IC3). Three bundles are marked: A is on IC1, B is on IC2 at the point where it is tangent to the
budget line, and C is on IC3 above the budget line.
(a) Which bundle is optimal? Explain why.
(b) Explain why bundle A is not optimal, even though it is affordable.
(c) Explain why bundle C is not optimal, even though it is on a higher indifference curve.
(d) What condition holds at the optimal bundle regarding the slope of the indifference curve
and the slope of the budget line? Express this condition in terms of MRS and PX/PY.
Q7.
(a) What does diminishing MRS mean in terms of the shape of indifference curves?
(d) Give an intuitive economic explanation for why consumers typically exhibit diminishing
MRS. What does it mean about how people value goods as they consume more of one
relative to the other?