PS7LT-2020.pdf - Microeconomics and Macroeconomics for...

Microeconomics and Macroeconomics for Public Policy (PP440)
Solution to Problem Set 7 - LT
Question 1
(a)
The household balance sheet looks as follows:
Assets ($) Liabilities ($)
House 1,000,000 Mortgage 800,000
Owner’s equity 200,000
Net wealth = Assets – Loans = 200 , 000
Leverage = Assets/ Equity = 1 , 000 , 000 / 200 , 000 = 5
(b)
The home improvement increases the value of the house to 1,100,000. The second mortgage increases the
liabilities of this family by 90,000. The new balance sheet looks as follows:
Assets ($) Liabilities ($)
House 1,100,000 Mortgage 1 800,000
Mortgage 2 90,000
Owner’s equity 210,000
Net wealth = Assets – Loans = 1 , 100 , 000 - (800 , 000 + 90 , 000) = 210 , 000
Leverage = Assets/ Equity = 1 , 100 , 000 / 210 , 000 = 5 . 238 > 5
The second mortgage increases the leverage of the family.
(c)
After the home improvement and house price decline of 20%, the value of the house declines to 1 , 100 , 000 ×
0 . 8 = 880 , 000. The new balance sheet is as follows:
Assets ($) Liabilities ($)
House 880,000 Mortgage 1 800,000
Mortgage 2 90,000
Owner’s equity -10,000
Net wealth = Assets – Liabilities = 880 , 000 - 890 , 000 = - 10 , 000 < 0
Alternatively, one can compute the change in equity as using the leverage ratio formula:
PercentChangeinEquity = ( PercentChangeinAssetvalue ) * Leverageratio
- 20% * 5 . 238 = - 104 . 76%
1

Hence, the new equity value is 210 , 000 - 210 , 000 * 1 . 0476 ≈ - 10 , 000. Since these mortgage contracts
are debt contracts, their value does not change with the house price. The borrower has to pay the same
amount independent of what happens to house process. That is, the borrower bears the whole house price
risk, which is further amplified because of leverage.
(d)
As house prices decline, homeowners’ wealth declines. The decline in wealth lowers demand for houses and
gives rise to a further decline in house prices and leads to a vicious cycle of depressed housing demand, low
house prices and declining wealth.
The decline in housing demand is more significant for the families that bought their houses with a
mortgage compared to those that do not have a mortgage. This is because loss in the value of the asset (in
this case house) implies a high decline in net wealth due to leverage.