solve for equilibrium loan rate and stock of money

(a) Explain the term monetary policy impotency. [5 marks]
(b) Assume an economy in which the demand for bank loans is given by:

and in which the portfolio preferences of the public generate a supply of bank deposits given by:

Where is the interest rate charged on bank loans, is the interest rate paid on bank deposits and i is the ‘market’ interest rate (and interest rates are measured in percentage points so that a rate of two per cent is given as 2, not 0.02).
The banks hold no reserves and have no other assets and liabilities and incur operating costs of $60 a year for every $1,000 of deposits.
(i) Assuming the banking system is competitive, solve for the loan rate and the deposit rate as functions of the market interest rate. Hence determine the stock of money in equilibrium [6 marks]
Imagine that the banks were now to collude and reach an agreement to set loan and deposit rates which maximize the profits of the industry.
(ii) Compute the optimal loan and deposit rates they will set [4 marks]
(iii) Calculate the profits of the industry [2 marks]
(iv) What are the effects of this cartel on the stock of money? [3 marks]
Assume that the government can influence the ‘market’ interest rate through its dealings in the gilt-edged money markets.
(v) Explain the effect of a change in the market interest rate on deposit and loan rates and on the stock of money and hence discuss the effectiveness of this monetary policy. [5 marks]
[Total 25 marks]
Due Date 23 March 2016