a)
The equilibrium values of output, real interest rate, price level, consumption and investment and the equation of IS curve, LM curve and the aggregate demand curve.
a)
Explanation of Solution
An economy with the following equations is presented:
Desired consumption
Desired investment
Real money demand
Full employment output
Expected inflation
Using the equation
Substituting the desired consumption and investment and solving for Y
Setting the real money demand to
The aggregate demand curve is
The equilibrium interest rate is
The equilibrium value of the price level is
The equilibrium value of consumption is
The equilibrium value of investment is
Substituting the given values of T and G into the general IS equation to obtain the IS curve equation
Equation is
Substituting the value of M into the Lm equation to obtain the equation for LM curve,
Thus, the equation for LM curve is
Using the IS and LM equations to find out the aggregate demand equation
Solving the IS equation for 2000r,
Equating the IS and LM equations, following is derived:
Thus, the aggregate demand curve is
Substituting the full employment output into the IS equation to obtain the real interest rate.
Therefore, the equilibrium interest rate is 0.1.
Using the aggregate demand curve to obtain the price level,
Substitute the full employment output value.
The equilibrium price level is 17
To obtain the value of consumption, substitute the given values of output and tax and the calculated value of interest rate into the desired consumption equation
The equilibrium consumption is 600
Substituting the value of real interest rate into the desired investment equation to obtain the equilibrium investment value
Thus, the equilibrium investment is 200
b)
The equilibrium values of output, real interest rate, price level, consumption and investment and the equation of the aggregate demand curve.
b)
Explanation of Solution
An economy with the following equations is presented:
Desired consumption
Desired investment
Real money demand
Full employment output
Expected inflation
Using the equation
Substituting the desired consumption and investment and solving for Y
Setting the real money demand to
The new aggregate demand curve is
The equilibrium price level is P=20
Now, the money supply has increased to M=9000
Use the IS and LM equations to find the new aggregate demand equation
By substituting, following is derived:
Multiplying the LM equation by 4 and solving it for 2000r
Solving the IS equation for 2000r
Equating the IS and LM equations, following is derived:
Thus, the new aggregate demand curve is
The change in money supply does not affect the equilibrium values of real interest rate consumption or investment
Therefore, using the aggregate demand curve to obtain the value for price level.
The equilibrium price level is 20.
c)
The equilibrium values of output, real interest rate, price level, consumption and investment and the equation of the aggregate demand curve.
c)
Explanation of Solution
An economy with the following equations is presented:
Desired consumption
Desired investment
Real money demand
Full employment output
Expected inflation
Using the equation
Substituting the desired consumption and investment and solving for Y
Setting the real money demand to
The aggregate demand equation is
The equilibrium value of real interest rate is
The equilibrium value of price level is
The equilibrium value of consumption is
The equilibrium value of investment is
The values for taxes have increased to
Recalculating the IS equation
The equation for LM curve remains the same.
Using the M and IS equations to find the aggregate demand equation,
Multiplying the Lm equation by 4 sand solving for 2000r.
Solving the IS equation for 200r
Equating the IS and LM equations
The aggregate demand equation is
Substituting the given full employment output into the IS equation to obtain the real interest rate
The equilibrium value of real interest rate is therefore 0.15.
Using the aggregate demand curve for obtaining the value of price level,
The equilibrium value of price level is 18.
Substituting the values of output and tax and calculated value of real interest rate into the desired consumption to obtain the value of consumption,
The equilibrium value of consumption is therefore 525
Using the desired investment equation to find the equilibrium value of interest
The equilibrium value of investment is 175.
Want to see more full solutions like this?
Chapter 10 Solutions
Pearson Etext For Macroeconomics -- Access Card (10th Edition)
- State whether the following statements are true, false, or uncertain and explain. -In the sticky-price model, if the economy is in a liquidity trap, the price level, P1, will display a tendency to fall. -Over the past 40 years, the average inflation rate was 3 per cent in country A and 22 per cent in country B. Country B must have had a lower average nominal interest rate than country A.arrow_forwardPlease solve all the three Multiple choice questions mentioned below: 1. Question in the image: a. Not exist b. will be horizontal c. Upward sloping like the usual LM curve d. None of the above 2. If in the short run, IS LM equilibrium occurs at a level of income above the natural rate of output, in the long run the output will return to the natural rate via: a. an increase in the price level b. a decrease in the interest rate c. an increase in the money supply d. a downward shift in the consumption function 3. Suppose that there are two countries, B and C, that have no trade and no financial transactions with any other countries except each other. B imports a total of goods worth 10 million 'bollars' from C, where a bollar is a unit of B's currency. B has no exports. Which of the following must be true? a. B has a capital account deficit b. C has a current account deficit c. C is buying assets from B d. The exchange rate of collars per bollar is bigger than 1, where collar is C's…arrow_forwardContinuing to work with a 2% inflation target, a 1999 version of the Taylor Rule and an initial nominal policy rate of 1.5%, now consider the impact of including a variable risk premium that is typically positive, meaning that the market interest rate is usually above the central bank policy rate. In the following questions, assume the normal (natural) risk premium is 100bp, the economy has a negative output gap (minus 1%), the actual risk premium is 300bp, the economy’s natural real market interest rate is 2% and that both actual and expected inflation is 1%. 5a) what nominal policy rate would you recommend? 5b) what is the natural nominal policy interest rate? 5c) how does the new market real interest rate compare with its initial level? 5d) what nominal policy rate would the Taylor Rule recommend if the negative output gap then widened to minus 2% and both current and expected inflation fell to zero? (other factors, including the risk premium remaining unchanged)arrow_forward
- Suppose the current level of output and the interest rate are such that the economy is operating on neither the IS nor LM curve. Which of the following is true for this economy? A) Production does not equal demand. B) The money supply does not equal money demand. C) The quantity supplied of bonds does not equal the quantity demanded of bonds. D) Financial markets are not in equilibrium. E) all of the abovearrow_forwardChapter 14, Problem 5, p. 530. (not answered) In the New Keynesian model, how should the central bank change its target interest rate in response to each of the following shocks? Use diagrams and explain your results. (a) There is a shift in money demand. (b) Total factor productivity is expected to decrease in the future. (c) Total factor productivity decreases in the present Chapter 14, Problem 6, p. 530. (not answered) In the New Keynesian model, suppose that in the short run the central bank cannot observe aggregate output or the shocks that hit the economy. However, the central bank would like to come as close as possible to economic efficiency. That is, ideally the central bank would like the output gap to be zero. Suppose initially that the economy is in equilibrium with a zero-output gap. (a) Suppose that there is a shift in money demand. That is, the quantity of money demanded increases for each interest rate and level of real income. How well does the central bank perform…arrow_forwardSuppose an economy is characterized by the following three equations: where the first equation is an aggregate-supply function written in the form of an expectations-augmented Phillips curve, the second is an IS or aggregate-demand relationship, and the third is a money-demand equation, where ∆m denotes the growth rate of the nominal money supply. The real interest rate is denoted by r and the nominal rate by i, with Let the central bank implement policy by setting i to minimize the expected value of Assume that the policy authority has forecasts ef , uf , and vf of the shocks but that the public forms its expectations prior to the setting of i and without any information on the shocks. a. Assume that the central bank can commit to a policy of the form prior to knowing any of the realizations of the shocks. Derive the optimal commitment policy (i.e., the optimal values of c0, c1, c2, and c3). b. Derive the time-consistent equilibrium under discretion. How does the…arrow_forward
- In the basic New Keynesian model, if the central bank is initially achieving its goals, and the natural rate of interest rises, the central bank should A. increase the nominal interest rate by the amount of the natural real interest rate increase. B. reduce the nominal interest rate by the amount of the natural real interest rate increase. C. increase the nominal interest rate by less than the amount of the natural real rate of interest increase. D. reduce the nominal interest rate by less than the amount of the natural real interest rate increase. E. do nothingarrow_forwardWhen workers do not notice inflation has taken place they do not realize that their real wage has declined. This phenomenon is consistent with which reason for the upward slope in the SRAS curve? mispreceptions the interest rate effect menu costs the principle-agent problemarrow_forwardAccording to the Keynesian ideas on Aggregate Demand, a macroeconomist would most likely expect business expenditure to increase when ... Group of answer choices a. Interest rates are low and expected returns are low b. Interest rates are high and expected returns are high c. Interest rates are low and expected returns are high d. Interest rates are high and expected returns are lowarrow_forward
- Which of the following is true of Advantages of the US implicit Nominal Anchor? Select one: a. The Fed’s forward-looking behavior and stress on price stability also help to discourage overly expansionary monetary policy, thereby ameliorating the time consistency problem. b. It does not enable monetary policy to focus on domestic considerations. c. It relies on a stable money-inflation relationship. d. None of the abovearrow_forwardIn the basic New Keynesian Model, in a liquidity trap where initially there is a positive output gap and inflation is lower than the inflation target, forward guidance is a promise by the central bank of A. lower future output than would otherwise be optimal for the central bank. B. lower current output. C. higher future inflation than would otherwise be optimal for the central bank. D. lower future inflation than would otherwise be optimal for the central bank. E. lower current inflation.arrow_forward
- Economics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage Learning