This problem revolves around determining the LM curve, as we did earlier in the term such that money demand (M^{D}) equals money supply (M^{S}), however in this instance under differing conditions of the interest elasticity of money demand. Suppose that money demand is given by:
M^{D} = [YF/2R_{o}]^{½}
Where Y is income, F is the transactions cost, and R_{o} is the opportunity cost of holding money. Assume that R_{o} is given as:
R_{o} = q_{1}R - q_{0}
In the equation above, R is the market interest rate and q_{1} and q_{0} are interest elasticity parameters in the opportunity cost of holding money expression.
a. Assume F = 2 and the parameters q_{1} = 1 and q_{0 }= 0.06 initially. What is the level of money demand, M^{D} if Y = 2,500 and R = 0.08? (Hint: Start with the R_{o} expression first, and then M^{D}).
b. Next, as we know in the determination of the LM curve (M^{S}_{ }= M^{D}), suppose that money supply is set equal to the value of M^{D} found in (a) to insure this equality. Now find the two market interest rates (R_{1} and R_{2}) at which money supply (M^{S}) equals money demand (M^{D}) when
Y = 1,000 and Y = 4,000. Plot (roughly sketch) what this LM curve would look like graphically (call this LM_{1}).
c. With F = 2 but assuming that the interest elasticity parameters of money demand change such
that q_{1} = 0.25 and q_{0 }= 0, repeat the process from above. Specifically, find the level of money demand (M^{D}) when Y = 2,500 and R = 0.08 (beginning with R_{o}). Similarly, supposing that money supply is set equal to this value of M^{D}, find the market interest rates (R) for the values of Y = 1,000 and Y = 4,000 as you did in part (b), and then plot (roughly sketch) what this LM curve would look like graphically in the same quadrant (call this LM_{2}).
d. For which values of q_{1} and q_{0} will the LM curve be steeper? Explain (or provide) a brief economic interpretation. How might the effectiveness of fiscal policy (i.e., ?IS) be impacted by these differing LM curves? Briefly explain.