CHAPTER 4
WORKING WITH SUPPLY AND DEMAND
EVEN NUMBER ANSWERS, SOLUTIONS, AND EXERCISES
PROBLEM SET
2. a. Your equity in the home is now $150,000, since $500,000 - $350,000 = $150,000.
b. At the end of the three years, you are 3.33 times leveraged, since $500,000/$150,000=3.33.
c. If the total debt associated with your home is $350,000, then your equity is wiped out if the price
of your home falls to $350,000, a 30% fall. If we start with a price of $500,000, a fall to $350,000
would be a 30% fall in the price, since ($500,000-$350,000)/$500,000 = 0.30.
4. a. Before any changes in price, the value of equity is equal to the down payment, $100,000.
b. Before any changes in price, the simple leverage ratio is $400,000/$100,000 = 4.
c. The new value of your equity is $500,000 - $300,000 = $200,000. The new simple leverage ratio is
$500,000/$200,000 = 2.5.
d. False. As you can see from parts b. and c., an increase in the value of a home, with no additional
borrowing or repayment, decreases the degree of leverage on the investment in the home. (However,
note that if the initial leverage was 1, then a change in price does not change the simple leverage
ratio. You can work this out on your own.)
6. For the following answers assume that the existing stock of homes in Monotone, AZ is Q.
a. We start off at point A, where the housing market in Monotone is in equilibrium. Without the
special tax breaks, 500 new homes would be built in Monotone (dashed vertical supply curve to the
right of S1). With the special tax breaks we observe an additional 300 new homes built, resulting in a
new stock of Q+800 homes (vertical supply curve S2). The special tax breaks only affect the home
builders, i.e. suppliers, and have no effect on demand. Demand, as usual in Monotone, shifts to the
right by 500 homes. Since supply shifted to the right by more than demand, the price of homes in
Monotone will fall from P1 in the old equilibrium (point A) to P2 in the new equilibrium (point C).
a) Tax Breaks for Home Builders
a. If interest rates fall, it effectively becomes cheaper to buy a house, thus shifting demand for homes
to the right by more than 500 (D1 shifts to D2). The vertical supply curve however only shifts to the
right by 500 homes, as usual for Monotone. Since there is a greater rightward shift in demand than in
supply, the price of homes increases from P1 to P2, as we move from the old equilibrium (point A) to
the new equilibrium (point C).
b) Interest Rates Fall
b. If zoning laws prevent construction of new homes in Monotone, the supply curve is fixed at S 1,
while the demand shifts rightward from D1 to D2 by 500 homes, as usual. This will lead the price to
increase from P1 to P2.
c) Zoning Laws – No New Construction
c. If in addition to zoning laws, home buyers’ expectations about the future go up (i.e. they expect
their homes to be more valuable in the future) then demand shifts to the right by more than 500
homes. As in part c. supply is fixed at S1, but demand shifts from D1 to D2. The resulting price P2 is
even higher than in part c.
d) Zoning and Expectations Go Up
d. We assume that before the earthquake, both the supply and demand in Monotone shifted to the
right by 500, as usual (S1 shifts to S2 and D1 shifts to D2). The earthquake destroys 2,000 homes,
shifting supply to the left to S3. At the same time 3,000 homeowners decide they don’t want to own
homes in Monotone, shifting demand to the left to D3. The resulting price, P2 is lower than the
original P1.
e) Earthquake, People Leaving
8. For the following answers assume that the existing stock of homes in Houseville, CA is Q.
a. We start at equilibrium point A, where the price of home is P1 and the stock of homes is Q.
Because Houseville won the award, demand shifts to the right by 5,000 homes (3,000 more homes
are demanded than usual). The award doesn’t affect supply, hence supply increases by the usual
2,000 homes. The new equilibrium point is C and the resulting price P2 is greater than P1.
b. Relaxation of restrictions by the city council does not affect the equilibrium price. Even though
home builders are now allowed to build up to 3,000 new homes, they choose to build only 2,000 new
homes, just enough to meet the increase in demand. Both supply and demand shift to the right by
2,000, moving us to the new equilibrium point C, at which price P1 is the same as it were at the old
equilibrium point A.
c. Home builders in Houseville build 2,000 new homes as usual (dashed vertical line at Q+2000), but
then an earthquake destroys 1,000 homes in Houseville, resulting in supply curve S2. Because of the
city council restriction, Houseville’s home builders are not allowed to build new homes to
compensate for the earthquake, so supply remains at Q+1000 (S2). The demand for homes in
Houseville is unaffected and shifts to the right by 2,000 homes as usual (D1 shifts to D2). The
resulting equilibrium is at point C, and price P2 is greater than P1, at the old equilibrium (point A).
d. If events in a., b. and c. all happen at the same time, the new housing stock would be Q+2000
homes (Q existing homes – 1000 destroyed in earthquake + 3000 new homes built, the maximum
allowed by city council = Q+2000). Said differently, the supply of homes would shift to the right by
2,000, resulting in S2. Demand would shift to the right by 5,000, because of Houseville’s award.
Since the rightward shift in demand exceeds the rightward shift in supply, the new equilibrium price
P2 is higher than P1.
10. a. If you default on your mortgage loan you basically only lose the $20,000 down payment
(assuming we neglect any mortgage payments made during the time between home purchase and
default, which are also lost). Hence, if falling housing prices decrease the value of your home to
anywhere below $180,000, you would want to default. This is achieved for any price decrease greater
than 20,000/200,000 = 10%.
b. If we assume that defaulting on your mortgage means that you lose $20,000 as well as an
additional $10,000, then you would default if the housing prices fell by more than 30,000/200,000 =
15%
MORE CHALLENGING
12. No. The minimum possible leverage is 1, which is the case in which you finance your home
purchase only with your own funds (i.e. no mortgage). In that case the value of the home is equal to
the equity, and the leverage ratio is 1. The only way to get the leverage ratio of ½ would be if equity
exceeds the value of the home, which, by definition of equity, is impossible.