solving for the values as simplied fractions ( 7 9 rather than 56 72 ), as opposed to decimals, will provide 'cleaner' solutions.
Consider the following Real Money Demand Function: L(Y; i) = 1000+0:3Y ??4000i, where i is the interest paid on non-monetary assets, P is the price level, Y is real income, and monetary assets earn no interest.
a) i) For P = 110; Y = 2000 and i = :05, nd equilibrium levels of real money (MR), nominal money (MN) and the velocity of money (V ).
ii) Assume real income increases by 5% and the nominal interest rate increases by 15%. Find the new levels of MR;MN and V .
iii) Now assume that Y falls by 10% from part (i) levels, and i falls by 30% from part (i) levels. Find the new levels of MR;MN and V .
iv) Derive the formula for the income elasticity of money demand as a function only of Y ,Y (Y ), and nd the value of Y (Y ) for parts (i) and
(ii). Derive the formula for the interest elasticity of money demand as a function only of i, i(i), and nd the value of i(i) for part (iii).
b) i) Does the Quantity Theory of Money hold in this question? Why or why not? Find a functional relationship between Y and i, expressed as a function Y (i), such that the Quantity Theory of Money would hold (remember that the k in the equation is a constant). What would part (a) section (i) suggest about the value of k in the Quantity Theory?
ii) If the Central Bank in uenced the nominal rate in such a way as to make the Quantity Theory of Money hold true (to your answer in the previous section), then what level of i (as a percentage) would they target in part (a) section (ii) given they could perfectly foresee the 5% increase in real GDP? What would be the new nominal level of money in the economy (with sticky prices)? If the Central Bank controls money supply directly, assuming the economy is in equilibrium with prices stuck at 110, by what percentage would the Central Bank need to increase the money supply to achieve their target level of i.
(We are always in equilibrium here, so Md = M)? If prices are sticky, what relationship does the Quantity Theory of Money suggest between the equilibrium money stock and interest rates?