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Macroeconomic Theory I - ECO 2142

Spring 2022 Assignment 2

Problem

Consider the following open economy (Home economy). The real exchange rate is ﬁxed and equal to one. Saving, investment, government spending, taxes, imports and exports are given by:

S = -80 + 0.18Y

I = I

G = G

T = T0 + t1Y

Q = q1Y

X = x1Y*

(1)

where T0 is the level of autonomous taxes, q1 and x1 are , respectively the marginal propensity to import, and export reaction to the foreign country’s income. An asterisk is used to designate variables related to the foreign economy.

1. Find the expression of saving (S) in terms of t1, c1, c0, and T0, assuming that the consump- tion function has the following expression: (8 points)

C = c0 + c1 (Y - T)

2. Assuming that t1 = 0.1, and T0 = 100, ﬁnd the values for the values of c0 and c1 . (6 points)

3. Solve for equilibrium income in Home economy, in terms of I, G, T0, t1, q1, x1, and Y* . (12 points)

4. Assuming that q1 = 0.1 and x1 = 0.1, ﬁnd the value of the multiplier for autonomous taxes (T0) in Home economy? (8 points)

5. Assume Foreign economy has the same equations as Home economy. Moreover, use the following values for the remaining autonomous variables: I = 500, G = 500.

(a) Solve for the equilibrium values of income, Y, and Y* in both economies. (8 points)

(b) Find the tax multiplier for each economy now? (8 points)

(d) Find the equilibrium values for government and trade deﬁcits in each economy. (8 points)

6. Assume Home economy wants to increase GDP by 150.

(a) What is the necessary change in the level of autonomous taxes, AT0, assuming that Foreign economy does not change its spending or its autonomous tax level to achieve the target output? (8 points)

(b) Solve for net exports and the budget deﬁcit in each economy. How do they compare to the values found in (5)? If there is any difference, discuss it. (10 points)

7. Assume now that both countries want to achieve the same increase in their GDP. They want to coordinate changes in their levels of autonomous taxes to achieve the target out- put.

(a) Find the required change in autonomous taxes in each economy. (6 points)

(b) Solve for net exports and the budget deﬁcit in each economy. How do they compare to the values found in (6)? Discuss the difference if there is any. (10 points)