# Linear Algebra: Interest Rates and Cramer's Rule

For each output level Y, the IS curve defines the interest rate r at which the goods market clears:

Y(1-b)-G=I^0-ar,

where b is the marginal propensity to consume, G is the government spending, I^0 is the maximum investment level, and a is the responsiveness of investment to interest rates. The LM curve defines the interest rate at which the money market clears:

mY + M^0 - hr = M^8,

Where m is the responsiveness of the transactions demand for money to output, M^0 is the maximum liquidity demand, h is the responsiveness of liquidity demand to interest rates, and M^8 is the money supply.

a) Write down this system of equations in matrix form. Under what condition on the exogenous parameters can this system of two equations be solved for Y and r?

b) Using Cramer's rule, solve the system for Y and r when the condition in (a) is met.

c) What happens to the equilibrium interest rate r if government spending increases by ?G?

Please see the attached file for full equations.

© BrainMass Inc. brainmass.com June 4, 2020, 3:35 am ad1c9bdddfhttps://brainmass.com/math/linear-algebra/linear-algebra-interest-rates-cramers-rule-522487

#### Solution Preview

Please see the attached file.

The Railway Ticket System has been established in order to design the fully automated software for issuing the railway ticket. With the help of this software, acceptance of user information and issuing of Passenger Name Record can be done. It has been analyzed that the online ticketing system is helpful in reducing the time of issuing ticket. Nowadays, passengers can get all information related to the train through the internet. A railway ticketing system is efficient and provides easy and quick services to the passengers. Here, inconsistencies, ambiguities and omissions in the given plan of ticket issuing system have been analyzed. Along with this, recommendations in order to improve the railway ticketing system have been discussed in this paper.

There are several inconsistencies, ambiguities and omissions in the ticketing system. Ambiguities and omission include different points such as: customer can buy several tickets for the same destination together or they have to buy one at a time. In this type of situation, customers face problem and are not able to get full information related to ticket issuing. Moreover, other questions such as: Can customers cancel the request? If mistake has been done and how system will ...

#### Solution Summary

The interest rates and Cramer's rules are examined. The responsiveness of investments to interest rates are provided.