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

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Microeconomics and Macroeconomics for Public Policy (PP440)Solution to Problem Set 7 - LTQuestion 1(a)The household balance sheet looks as follows:Assets ($)Liabilities ($)House1,000,000Mortgage800,000Owner’s equity200,000Net wealth = Assets – Loans = 200,000Leverage = 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 theliabilities of this family by 90,000. The new balance sheet looks as follows:Assets ($)Liabilities ($)House1,100,000Mortgage 1800,000Mortgage 290,000Owner’s equity210,000Net wealth = Assets – Loans = 1,100,000-(800,000 + 90,000) = 210,000Leverage = Assets/ Equity = 1,100,000/210,000 = 5.238>5The 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 ($)Liabilities ($)House880,000Mortgage 1800,000Mortgage 290,000Owner’s equity-10,000Net wealth = Assets – Liabilities = 880,000-890,000 =-10,000<0Alternatively, 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 contractsare debt contracts, their value does not change with the house price.The borrower has to pay the sameamount independent of what happens to house process. That is, the borrower bears the whole house pricerisk, which is further amplified because of leverage.(d)As house prices decline, homeowners’ wealth declines. The decline in wealth lowers demand for houses andgives rise to a further decline in house prices and leads to a vicious cycle of depressed housing demand, lowhouse prices and declining wealth.The decline in housing demand is more significant for the families that bought their houses with amortgage compared to those that do not have a mortgage. This is because loss in the value of the asset (inthis case house) implies a high decline in net wealth due to leverage.

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