Question

Consider the New Keynesian model with completely sticky goods prices and flexible nominal wages introduced at the lecture. Suppose that central bank follows the policy of strict interest rate targeting. Firms must borrow to finance investment at interest rate rl since they do not have sufficient internal funds to finance investment. There is a spread x = rl − r > 0 between the interest rate rl and the interest rate r received by savers. To simplify the analysis assume zero depreciation rate and ignore the distortionary effect of the cash in advance constraint.

(a) Show using a proper model from our course how an expectation of a higher fraction of bad loans in the future will affect the interest rate spread. State the assumptions explicitly and justify every claim.

(b) Suppose that initially spread was zero but a financial crisis results in a positive interest-rate spread x>0. Show how this increase in the spread will affect (i) consumption and (ii) investment components of output demand. Demonstrate by the proper graphs from our course.

Answer 1

In the New Keynesian model, an expectation of higher bad loans will increase the interest rate spread. A positive interest rate spread due to a financial crisis reduces investment and consumption components of output demand.

Step-by-step explanation:

In the New Keynesian model with completely sticky goods prices and flexible nominal wages, an expectation of a higher fraction of bad loans in the future will increase the interest rate spread. This is because the expectation of higher bad loans increases the risk for lenders, leading them to charge a higher interest rate to compensate for the increased risk. The assumption here is that firms must borrow to finance investment and that there is a spread between the interest rate paid by firms and the interest rate received by savers.

In the case of a positive interest rate spread due to a financial crisis, it will affect consumption and investment components of output demand. A positive interest rate spread makes borrowing more expensive for firms, reducing their incentive to invest in physical capital. Additionally, higher interest rates discourage consumer borrowing for big-ticket items, reducing consumption. These effects can be represented in the proper graphs from our course.