Question

Answer parts e-h

Problem 3: (30 points) Suppose we have an open economy with a government entity such that the economy is defined by the following functions: C = 100+ 0.5Yd i = 50 G = 100 a. Find the equilibrium level of income in this economy. (5 points) b. What is the multiplier in this economy? (3 points) c. Suppose governments transfers increases to 100, what is the effect of this change on the equilibrium level of income? What is the new equilibrium level of income? (5 points) d. Calculate the budget surplus. (2 points) e. Suppose the government decides to impose a proportional income tax (t) instead of lumpsum taxation such that t = 0.2. Calculate the equilibrium level of income in this model. (5 points) f. What is the multiplier in this case? (3 points) g. Calculate the budget surplus in this economy. (2 points) h. What is the change in budget surplus if the government increases its purchases for goods and services by 50? (5 points)

Answer 1

(e)

C = 100 + 0.5 x (Y + 50 - 0.2Y) = 100 + 0.5 x (0.8Y + 50) = 100 + 0.4Y + 25 = 125 + 0.4Y

In equilibrium, Y = C + I + G + NX

Y = 125 + 0.4Y + 50 + 100 + 30

0.6Y = 305

Y = 508.33

(f)

Multiplier = 1 / [1 - MPC(1 - t)] = 1 / [1 - 0.5(1 - 0.2)] = 1 / [1 - 0.5 x 0.8] = 1 / (1 - 0.4) = 1 / 0.6 = 1.67

(g)

T = 0.2 x 508.33 = 101.67

Budget surplus = TA - TR - G = 101.67 - 25 - 100 = - 23.33 (indicating budget deficit of 23.33)

(h)

When G increases by 50 (to 150), with proportional tax,

Y = 125 + 0.4Y + 50 + 150 + 30

0.6Y = 355

Y = 591.67

T = 0.2 x 591.67 = 118.33

Budget surplus = TA - TR - G = 118.33 - 25 - 150 = - 56.67 (indicating budget deficit of 56.67)

Change in budget surplus = - 56.67 + 23.33 = - 33.34