stion 14 of 15 > Macmillan Learning National Income: Where It Comes From and Where It Goes \textendash{} End of Chapter Problem Show on the graph how each of the following events changes the equilibrium interest rate by shifting the relevant curve(s). a. The president signs a tax cut into law. Interest rate 10 9 S 8 7 6 5 4 3 2 1 D 0 100 200 300 400 500 600 700 800 900 1,000 Loanable funds
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12. Consider the National Income Model: Y = C + I + G C = a + b (Y - T), I = I₀ - lr + qY where the government can also run a deficit as a percentage of income. D = (G - T) = uY where T = tY are taxes as a fraction of income. The u, a, b, l, I₀, q and t are positive scalars. C= consumption, I=investment, G=government spending, Y= income, and r= rate of interest. a. List the endogenous/exogenous variables and parameters? b. Place system in matrix form Ax = d c. Solve for equilibrium endogenous variables via Cramer’s rule. d. What is the equilibrium effect of increasing government spending through a taxes on income? e. What is the equilibrium effect of increasing government spending though deficit spending on income? f. Provide intuition for (d) and (e) and compare the two approaches to raising gov’t spending.
Akash M.
1. An economy is described by the following equations: C =500 + 0.75(Y − T ) I =1, 000 − 50r M/P =Y − 200r G =1, 000 T =1, 000 M =6, 000 P =2 a. Drive and graph the IS curve and the LM curve. Calculate the equilibrium interest rate and income. Label that point A on your graph. b. Suppose a newly elected president cuts taxes by 20%. Assuming that the money supply is held constant, what are the new equilibrium interest rate and income? What is the tax multiplier? c. Now assume that central bank adjust the money supply to hold the interest rate constant. What is the new equilibrium income? What must the new money supply be? What is the tax multiplier? d. Now assume that the central bank adjust the money supply to hold income constant. What is the new equilibrium interest rate?What must the money supply be? What is the tax multiplier?
Breanna O.
Exercises 17 and 18 concern a simple model of the national economy described by the difference equation $$ Y_{k+2}-a(1+b) Y_{k+1}+a b Y_{k}=1 $$ Here $Y_{k}$ is the total national income during year $k, a$ is a constant less than $1,$ called the marginal propensity to consume, and $b$ is a positive constant of adjustment that describes how changes in consumer spending affect the annual rate of private investment. Find the general solution of equation $(14)$ when $a=.9$ and $b=\frac{4}{9} .$ What happens to $Y_{k}$ as $k$ increases? [Hint: First find a particular solution of the form $Y_{k}=T,$ where $T$ is a constant called the equilibrium level of national income. 1
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