Suppose that loan demand is given by Loans Demanded=d0+d1×Y-d2 r

Loans Demanded=2025+0.05×Y-0.01r

Also, suppose that the loan supply is

Loans Supplied=s0+s1 (r-rrf )

Loans Supplied=75+1000(r-rrf )

a). Write out a numerical relation between the equilibrium interest rate, the risk-free rate, and output. That is, take this equation

r=1/(s1+d2 ) (d0-s0 )+s1/(s1+d2 ) rrf+d1/(s1+d2 ) Y

which is Equation 4 in the chapter? Use the parameters in the equations for Loan Demand and Loan Supply to calculate each of the terms. That is, calculate s1+d2, then calculate 1/(s1+d2 ), then calculate 1/(s1+d2 ) (d0-s0 ), then s1/(s1+d2 ) and d1/(s1+d2 )

The result should be an equation that has on the left-hand side and three terms on the right-hand side: a constant number, a number times the risk-free rate, and a number times output.

S1 = 1,000 1/1000.01 (2025-75)

d2 = 0.01

b). Assume $Y is $200 and rrf is 2.0% = 0.02. What is the equilibrium interest rate ?

c). If the Federal Reserve Bank wants to make the equilibrium interest rate 4 percent. That is, r=0.04 . Use the numerical equation you found in part (a) to solve for the needed value of the risk-free interest rate.

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