Chapter 4.6, Problem 61E

Exercises 61 and 62 are based on the following demand function for money (taken from a question on the GRE Economics Test):

$M_d=\left(2\right)\times {\left(y\right)}^{0.6}\times {\left(r\right)}^{-0.3}\times \left(p\right),$

Where

$M_d=$ demand for nominal money balances (money stock)

$y=$ real income

$r=$ an index of interest rates

$p=$ an index of prices.

Money Stock If real income grows while the money stock and the price level remain constant, the interest rate must change at what rate? (First find $dr/dy$, then find $dr/dt$; your answers will be expressed in terms of r, y, and $dy/dt$.)