Tutorial 5
Chapter 7: Borrowing, lending, and budget constraints
Multiple choice questions
Consumption tomorrow
Question 1
D
M
Y2
A
slope =-(1+r)
0
Y1
B
Consumption today
Point A represents the endowments of Crusoe for today and tomorrow, the real
interest rate is r, and we observe that Crusoe consumes at point M. From this
information what do we know about Crusoe?
a. That he needs to borrow in order to finance his higher consumption planned
tomorrow.
Feedback: Incorrect. Today, he will save, in order to consume more tomorrow.
Page reference: 158
b. That he faces a liquidity constraint tomorrow that makes point M infeasible.
Feedback: Incorrect. One may always save what one wants: there is no ‘saving
rationing’.
Page reference: 158
c. That he has a present discounted wealth equal to OD.
Feedback: Incorrect. That would be OB.
Page reference: 158
*d. That he saves today.
Feedback: Correct. He will thus be able to finance consumption tomorrow in excess
of tomorrow’s income.
Page reference: 158
Question 2
The following data are relevant for Crusoe’s intertemporal budget constraint: 150 is
the present endowment; 110 is the future endowment; 0.1 is the real interest rate (i.e.
10 per cent) between the present and the future. Crusoe’s wealth consequently equals
which ONE of the following?
a. 130
Feedback: Incorrect. Wealth is not the average endowment.
Page reference: 161
*b. 250
Feedback: Correct. Wealth is the present discounted value of the endowments.
Page reference: 161
c. 260
Feedback: Incorrect. Wealth is not the sum of the endowments.
Page reference: 161
d. His wealth cannot be determined using only the information given here.
Feedback: Incorrect. It can, indeed, be determined using this information.
Page reference: 161
Consumption tomorrow
Question 3
D
Y2
A
slope = - (1+r )
0
Y1
B
Consumption today
Y1 is the present endowment; Y2 is the future endowment; r is the real interest rate
between the present and the future. If the real interest rate should increase, which
ONE of the following will be true of intertemporal budget constraint?
a. It will rotate counterclockwise from point D.
Feedback: Incorrect. It will rotate clockwise through point A.
Page reference: 159–60
b. It will rotate clockwise from point B.
Feedback: Incorrect. It will rotate clockwise through point A.
Page reference: 159–60
*c. It will rotate clockwise through point A.
Feedback: Correct. Higher r means that the intertemporal budget constraint gets
steeper. It has to rotate through A, because one can always consume one’s own
endowment!
Page reference: 159–60
d. It will rotate counterclockwise through point A.
Feedback: Incorrect. It will rotate clockwise through point A.
Page reference: 159–60
Consumption tomorrow
Question 4
D´
E
D
F
Y =F(K )
A
Y2
K
0 C1
Y1
B B´
Consumption today
The figure above represents a two-period world with an initial endowment A and a
productive technology, in which Y1 is today’s endowment, Y2 is tomorrow’s
endowment, and the curved line through points A and E relates investment in capital
through saving today in order to produce tomorrow. The fact that point B´ lies to the
right of point B means which ONE of the following?
a. Technological change has shifted the intertemporal budget constraint.
Feedback: Incorrect. See Figure 7.5.
Page reference: 164
*b. Investing in a productive technology allows a household to increase its wealth.
Feedback: Correct. This is Figure 7.6.
Page reference: 164
c. Investment demand has increased the interest rate.
Feedback: Incorrect. The slopes of DB and D´B´ are the same.
Page reference: 164–5
d. The household could do even better by borrowing to increase today’s consumption.
Feedback: Incorrect. This means consuming along AB, which is below EB´.
Page reference: 164–5
Question 5
Consider the government budgets for a two-period model, in which: T1 is today’s net
taxes; T2 is tomorrow’s net taxes; D1 is government debt at the start of today; D2 is
government debt at the start of tomorrow; G1 is today’s government spending; G2 is
tomorrow’s government spending; rG is the real interest rate paid on government debt.
All variables are positive. Which ONE of the following does the government’s
intertemporal budget constraint require?
*a. D1 + G1 + G2/(1 + rG ) = T1 + T2/(1 + rG)
Feedback: Correct. The present value of revenues (right-hand side) is equal to the
present value of spending and inherited obligations (plus interest).
Page reference: 167
b. D1 + D2/(1 + rG) + G1 + G2/(1 + rG) = T1 + T2/(1 + rG)
Feedback: Incorrect. This is not the present value of spending and inherited
obligations (plus interest) equal to the present value of revenues.
Page reference: 167
c. G1 + G2/(1 + rG) – (T1 + T2/(1 + rG)) = (D1 + D2/(1 + rG))
Feedback: Incorrect. This is not the present value of spending and inherited
obligations (plus interest) equal to the present value of revenues.
Page reference: 167
d. D1 + G1 + T1 = (D2 + G2 + T2)/(1 + rG)
Feedback: Incorrect. This is not the present value of spending and inherited
obligations (plus interest) equal to the present value of revenues.
Page reference: 167
Question 6
The Ricardian equivalence proposition, if true, would be consistent with which ONE
of the following?
a. The government and the private sector facing different interest rates in their
intertemporal trade.
Feedback: Incorrect. The same interest rate is a required assumption for Ricardian
equivalence.
Page reference: 170-71
b. The existence of capital market imperfections that limit some households access to
credit.
Feedback: Incorrect. The absence of such capital markets imperfections is a required
assumption for Ricardian equivalence.
Page reference: 171
c. Governments financing themselves through a pyramid scheme.
Feedback: Incorrect. Governments are assumed to satisfy their own intertemporal
budget constraints.
Page reference: 175
*d. Representative households not regarding government bonds as part of their net
wealth.
Feedback: Correct. The private sector can see through the veil of government, i.e.
debt now is future taxes: ‘Pay me now or pay me later—but you will pay me’!
Page reference: 169-170
Open question: Exercise 3 from the book.
3. If 10% of the coconuts are lost (or “depreciate”) each period, the real interest rate is
negative and equal to –10%: one coconut saved today yields 0.9 coconuts tomorrow.
The slope of the budget constraint is less than 1 in absolute value. Since Crusoe
cannot borrow by assumption here, the budget line is truncated at his endowment
point A (he cannot consume today more than today’s endowment).
Opening the market for loans – even at a high interest rate – allows Crusoe to convert
some of the future income into the present. If Crusoe is impatient, access to a market
for loans will make him better off, since he can always choose not to borrow.
Open question: Exercise 5 from the book.
5. The net present value of the firm is the discounted sum of all expected future
payments, i.e. dividends plus resale value, less the initial investment. If it is positive,
the investment is worth undertaking under conditions assumed.
Extra question: Exercise 9 from the book.