Assume that the money demand function is (M/P)^d = 2,200

Question

Assume that the money demand function is (M/P)^d = 2,200 - 200r, where r is the interest rate in percent. The money supply M is 2,000 and the price level P is 2. If the price level is fixed and the supply of money is raised to 2,800, then the equilibrium interest rate will: A) drop by 4 percent. B) drop by 2 percent. C) drop by 1 percent. D) remain unchanged.

Quizplus · Accepted Answer

We can start by using the quantity theory of money equation: M × V = P × Y Where M is the money supply, V is the velocity of money (assumed constant), P is the price level, and Y is real output. Assuming Y is fixed, we can rewrite the equation as: (M/P)d = 1/V Where d is the demand for money in real terms (i.e. (M/P)^d / P) and 1/V is the supply of real balances. Substituting the given values: d = (2,200 - 200r)/2 = 1,100 - 100r M/P = 2,000/2 = 1,000 d/M = (1,100 - 100r)/1,000 We can solve for the equilibrium interest rate by setting the supply of real balances equal to the demand for real balances: (2,800/2)d/2,800 = (2,000/2)d/2,000 1 - r/+ (Δd)/(d) = (M /+ (ΔM)) / P Simplifying: (1,100 - 100r)/1,400 = 1,100/1,000 r = 3 So the equilibrium interest rate drops by 2 percent (from 5 percent to 3 percent) when the money supply increases from 2,000 to 2,800, assuming the price level is fixed. Therefore, the correct answer is B.

Assume That the Money Demand Function Is (M/P)d = 2,200