Consider a closed economy. Consumption C is given by the consumption function

C = C0 + cY , where C0 denotes autonomous consumption demand, and c is the marginal propensity to consume (a number between 0 and 1). Investment I is given by the function I = I0 br, where I0 is autonomous investment demand, and b is the sensitivity of investment to the interest rate r. Government spending and taxes are exogenous. In this question, attention is restricted to a short enough period of time in which prices and wages do not adjust. Assume that monetary policy sets a constant interest rate r, which means that the LM curve is horizontal.

(a)[4 marks] Suppose there is a decline in autonomous investment demand I0 owing to a loss of confidence about the economy's future prospects. Find the effect on the economy's GDP using the IS-LM diagram.

(b)[8 marks] Solve the equation Y =C+I+G to find the size of the effect on GDP Y of a one-unit decline in I0. Is the size of the response of GDP larger or smaller than 1? Give an intuitive explanation of your answer.

In what follows, assume the central bank adjusts interest rates up or down in line with economic activity, that is, r moves in the same direction as Y .

(c) [4 marks] How does this change to the conduct of monetary policy affect the IS-LM diagram in part (a), and the size of the response of GDP to lower I0?

Now suppose a financial crisis occurs with many firms defaulting on their debts. Consequently, banks that lend to firms charge an interest rate rl on loans, where

rl = r + s, with s denoting the spread over the safe interest rate r on government bonds. Monetary policy continues to set r as before. For firms that need to borrow from the banks, investment demand is now I = I0 brl.

(d)[6 marks] Use the IS-LM model to find the effects of an increase in the interest rate spread s on Y, r, and rl.

(e)[4 marks] Following a rise in the spread s, what would the central bank need to do to prevent this affecting GDP?

(f)[4 marks] Suppose some firms can finance investment from retained earnings without needing to borrow, or if they need to borrow, they can post collateral. How might this change the size of the effect on GDP in part (d)?