Sometimes understanding of ISLM becomes clearer when one works through the algebra. This question is designed to promote such understanding. Consider Country A, a closed economy characterized by the following relationships: C = 200 + 0.5YD I = 70- 5r G = T = 100 MD = 500 + Y – 15i where YD, disposable income, is equal to income less taxes, Y-T, and r and i are the real and nominal interest rates expressed in percent. Country A is ruled by a fierce dictator who abhors price movements, so assume prices are not allowed to change in this economy, i.e., that i = r. a) Assume Y=600 and plot money demand as a function of the nominal interest rate (put MD on the x-axis and i on the y-axis). Plot a second money demand function assuming Y=450. Assume the Central Bank sets the money supply at 800. What is the equilibrium real interest rate if Y=600? If Y=450? (Do the relative levels of these interest rates make sense to you?) b) Assume that the money supply is 800. Derive algebraic expressions for the IS and LM curves, in each case expressing them as r equals some function of Y. Verify that they have the expected slopes. Graph them in an ISLM diagram. c) How is the slope of the IS curve related to the marginal propensity to consume? Using the information in part b plot the IS and LM curves in (r,Y) space. In doing so, find the equilibrium interest rate and output such that the goods and money markets are in equilibrium.
Sometimes understanding of ISLM becomes clearer when one works through the algebra. This question is designed to promote such understanding. Consider Country A, a closed economy characterized by the following relationships:
C = 200 + 0.5YD
I = 70- 5r
G = T = 100
MD = 500 + Y – 15i
where YD, disposable income, is equal to income less taxes, Y-T, and r and i are the real and nominal interest rates expressed in percent. Country A is ruled by a fierce dictator who abhors price movements, so assume prices are not allowed to change in this economy, i.e., that i = r.
a) Assume Y=600 and plot money demand as a function of the nominal interest rate (put MD on the x-axis and i on the y-axis). Plot a second money demand function assuming Y=450. Assume the Central Bank sets the money supply at 800. What is the equilibrium real interest rate if Y=600? If Y=450? (Do the relative levels of these interest rates make sense to you?)
b) Assume that the money supply is 800. Derive algebraic expressions for the IS and LM curves, in each case expressing them as r equals some function of Y. Verify that they have the expected slopes. Graph them in an ISLM diagram.
c) How is the slope of the IS curve related to the marginal propensity to consume?
Using the information in part b plot the IS and LM curves in (r,Y) space. In doing so, find the equilibrium interest rate and output such that the goods and
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