Question

Suppose that desired consumption and desired investment are given as: C = c1 + cY (Y − T ) − cr r I = i1 − irr G = G0 T = τ1 + τ Y (a) Derive the equation for IS curve and draw its graph assuming c1 = 200 i1 =200 G=196 cY = 0.8 ir =500 τ1 =20 cr = 500 τ =0.25 (b) What would happen to the IS curve when lump-sum taxes, τ1, increases? (c) What would happen to the IS curve when income tax, τ, increases? Sabancı University Assignment 6 1. Consider labor market in an economy. In a classical model, you can think that each worker comes with one unit of effort. In a Keynesian model effort makes a difference. Suppose that the efficiency wage is above labor market equilibrium. (a) Draw a graph where you can show both employment and unemployment predicted by each model. Discuss unemployment under both models. (b) Now suppose a negative productivity shock hits the economy. How would employment and unemployment change under both Classical and Keynesian model. Show your results on a graph. (c) When the economy is hit by a negative productivity shock, workers are worried about their jobs and they start working harder, that is they increase their effort, say from two to three. (Note that in the Classical model this is not possible. their effort level is still unity.) How would this affect employment, unemployment and output in the Keynesian model? (d) The parliament passes a new law requiring balanced budget, that is G = T . How would this new law affect the IS curve? 3) In some macroeconomic models, desired investment depends on both the current level of output and the real interest rate. One possible reason that desired investment may depend on output is that, when current production and sales are high, firms may expect continued strong demand for their products in the future, which leads them to want to expand capacity. Algebraically, we can allow for a link between desired investment and current output by replacing the desired investment equation in the previous question with I = i1 − irr + iY Y, where iY is a positive number. Use this alternative equation for desired investment to derive the algebraic expressions for the IS curve.

Answer 1

1) Given:

C = c1 + cY (Y − T ) − cr

I = i1 − irr

G = G0

T = τ1 + τ Y

a) Derivation of IS curve equation:

Y= C+I+G

Y= c1 + cY (Y − T ) − cr + i1 − irr + G0

Y= c1 + cY (Y − τ1 - τ Y ) − cr + i1 − irr + G0

Y= 200+0.8(Y-20-0.25Y)-500r+200-500r+196

Y=596-1000r+0.6Y-16

Y-0.6Y=580-1000r

0.4Y=580-1000r

Y=1450-2500r (IS equation)

b) When lump-sum taxes, τ1, increases, It cause leftward shift of IS curve. Suppose τ1 increases to 50 then

Y= C+I+G

Y= c1 + cY (Y − T ) − cr + i1 − irr + G0

Y= c1 + cY (Y − τ1 - τ Y ) − cr + i1 − irr + G0

Y= 200+0.8(Y-50-0.25Y)-500r+200-500r+196

Y=596-1000r+0.6Y-40

Y-0.6Y=556-1000r

0.4Y=556-1000r

Y=1390-2500r (IS equation)

Initial IS curve is in Blue and new IS curve due to increase in T1 is in Green.

c)  When income tax, τ, increases, it cause IS curve to be more steep. Suppose T increases to 0.5

Y= C+I+G

Y= c1 + cY (Y − T ) − cr + i1 − irr + G0

Y= c1 + cY (Y − τ1 - τ Y ) − cr + i1 − irr + G0

Y= 200+0.8(Y-20-0.5Y)-500r+200-500r+196

Y=596-1000r+0.4Y-16

Y-0.4Y=580-1000r

0.6Y=580-1000r

Y=1966.66-1666.67r (IS equation)