Question

CALCULUS- compound interest and elasticity question?

Answer 1

Suppose the Canadian real estate market can be described by the following model. The price of the average detached single family house P = Pe + Pd consists of two components: the equity component Pe (this is the cash down-payment when you buy a house) and the debt component Pd (this is the amount financed by a loan). We assume that 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) If, however, 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 average house price P in this situation.