Assume that the following equations characterize a large open economy: (1) Y = (

Question

Assume that the following equations characterize a large open economy:

(1)     Y = (2G+ 3T)

(2)     Y = C + I + G + NX

(3)     C = 1/2(Y – T)

(4)     I = 2,100 – 100r

(5)     NX = 500 – 500e

(6)     CF = –200r

(7)     CF = NX

(8)     G = 1,500

(9)     T = 1,000.

Where NX is net exports, CF is net capital outflow, and e is the real exchange rate.

Solve these equations for the equilibrium values of C, I, NX, CF, r, and e. (Hint: Substitute equations (9) and (1) into (3), then substitute (1), (3), (4), (8), and (5) into (2). Then substitute (5) and (6) into (7). Now you have two equations in r and e. Check your work by seeing that all of these equations balance given your answers.)

Explanation / Answer

Y = 2G + 3T = (2 x 1,500) + (3 x 1,000) = 3,000 + 3,000 = 6,000

C = (Y - T) / 2 = (6,000 - 1,000) / 2 = 5,000 / 2 = 2,500

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

6,000 = 2,500 + 2,100 - 100r + 1,500 + 500 - 500e

6,000 = 6,600 - 100r - 500e

100r + 500e = 600

r + 5e = 6 [Dividing by 100]...........(1)

Again, NX = CF

500 - 500e = - 200r

200r - 500e = - 500

2r - 5e = - 5 [Dividing by 100]..........(2)

Multiplying (1) by 2,

2r + 10e = 12.........(3)

2r - 5e = - 5..........(2)

(3) - (2) yields: 15e = 17

e = 17 / 15 = 1.13

r = 6 - 5e [From (1)] = 6 - (5 x 1.13) = 6 - 5.65 = 0.35

Validation:

I = 2,100 - (100 x 0.35) = 2,100 - 35 = 2,065

NX = 500 - (500 x 1.13) = 500 - 565 = - 65

Y = C + I + G + NX

Y = 0.5Y - 500 + 2,065 + 1,500 - 65

(1 - 0.5)Y = 3,000

0.5Y = 3,000

Y = 6,000 [Verified]

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.