Answer to Question #17232 in Calculus for hsd

Question

The price of the average detached single family house P = Pe + Pd consists of two components: the equity component Pe (cash down-payment) and the debt component Pd (amount financed by a loan). The equity component is constant Pe = $200000 whereas the debt component follows an exchange equation MV = PdQ
at every time. Here, Q is the number of existing houses, M denotes the total amount of
mortgages held on the books of the banks, and V denotes the velocity of credit money in the
real estate market. We assume that V = 1=3 is constant. On January 1, 2012, Q is 5 million
units, growing at a rate of 50000 per year, and Pd is $200000.
(a) If the banks are reducing their lending standards such that M increases at a rate of $300 billion per year, at what rate (in percent) does the average house price P increase?
(b) there is no new mortgage lending and the current borrowers only pay back their existing loans, M decreases at a rate of $30 billion per year. Calculate the relative rate of change of the house P.