Exam



Practice Problems for Exam 2 – econ 304 – spring 2020

There are two types of problems on exam: Open Economy (the first 2 problems) and General Equilibrium (the second 2 problems)

1. (65 points total) We assume that the world consists of two large open economies, USA and China.

USA Initial Conditions

Cd = 420 + 0.5(Y-T) – 300rw

Id = 460 – 200rw

Y = 2400

T = 200

G =500

China Initial Conditions

Cd = 500 + .5(YF – TF) – 300rw

Id = 400 – 200rw

Y = 2000

T = 400

G = 300

a) (10 points) What is the equilibrium interest rate that clears the international goods market? Show all work

b) (5 points) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate .

c) (5 points) Which country is ‘spending beyond its means’ and which country is the saver? What exactly do we mean by the phrase ‘spending beyond its means’ in this context. Be sure to define and use the word absorption in your answer and compare absorption in each country to its income. Explain.

Draw two diagrams side by side, with the US on the left and the China on right. Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses.

20 points for correct and completely labeled diagrams

We now have a change in conditions: US experiences some economic growth and output rises to 2500. All else remains the same.

d) (10 points) Resolve for the world real interest rate that clears the international goods market along with the ‘new’ Sd and Id for each country and add these results to your diagram labeling this new equilibrium as points B on both of your diagrams. (10 points)

e) (5 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means. Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA). Are your results consistent with the US going to AA? Why or why not? Explain and please be specific.

f)(10 points) We know that world output has gone up by 100 and we also know, via the equation below that the world's absorption has to rise by 100 (right hand side of the equation below). Explain where this 100 in additional output was absorbed in each country. Use specific numbers.

Yus + YChina = [C + I + G] US + [C + I + G] China

2. (60 points total) We assume that the world consists of two large open economies, USA and China.

USA Initial Conditions

Cd = 400 + 0.5(Y-T) – 300rw

Id = 460 – 200rw

Y = 2400

T = 200

G =500

China Initial Conditions

Cd = 500 + .5(YF – TF) – 300rw

Id = 400 – 200rw

Y = 2000

T = 400

G = 300

a) (10 points) What is the equilibrium interest rate that clears the international goods market? Show all work

b) (5 points) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate .

c) (5 points) Which country is ‘spending beyond its means’ and which country is the saver? What exactly do we mean by the phrase ‘spending beyond its means’ in this context. Be sure to define and use the word absorption in your answer and compare absorption in each country to its income. Explain.

Draw two diagrams side by side, with the US on the left and the China on right. Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses.

20 points for correct and completely labeled diagrams

We now have a change in conditions: China experiences some economic growth and their output rises to 2100. All else remains the same.

d) (5 points) Resolve for the world real interest rate that clears the international goods market along with the ‘new’ Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams. (10 points)

e) (5 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means. Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA). Are your results consistent with the US going to AA? Why or why not? Explain and please be specific.

f)(10 points) We know that world output has gone up by 100 and we also know, via the equation below that the world's absorption has to rise by 100 (right hand side of the equation below). Explain where this 100 in additional output was absorbed in each country. Use specific numbers.

Yus + YChina = [C + I + G] US + [C + I + G] China

3. Suppose we have the following that describes the economy:

IS: Y = 12 – r

MP: r = 1 + .5 π

SRAS: π = πe + γ (Y – YP) + ρ

Given: πe = 2, γ = 1, YP = 10, ρ = 0

What is the equilibrium output, r, and π?

Now suppose that the IS curve changes and is now:

IS’: Y = 13 – r

What could cause such a change in the IS curve?

Find the new equilibrium output, r, and π?

Is this new equilibrium a long-run equilibrium? Why or why not?

Now find the long-run equilibrium output, r, and π?

4. Suppose we have the following that describes the economy:

IS: Y = 23 – r

MP: r = 2 + .5 π

SRAS: π = πe + γ (Y – YP) + ρ

Given: πe = 6, γ = 2, YP = 18, ρ = 0

What is the equilibrium output, r, and π?

Now suppose that the IS curve changes and is now:

IS’: Y = 21 – r

What could cause such a change in the IS curve?

Find the new equilibrium output, r, and π?

Is this new equilibrium a long-run equilibrium? Why or why not?

Now find the long-run equilibrium output, r, and π?

KEY

1. (65 points total) We assume that the world consists of two large open economies, USA and China.

USA Initial Conditions

Cd = 420 + 0.5(Y-T) – 300rw

Id = 460 – 200rw

Y = 2400

T = 200

G =500

China Initial Conditions

Cd = 500 + .5(YF – TF) – 300rw

Id = 400 – 200rw

Y = 2000

T = 400

G = 300

a) (10 points) What is the equilibrium interest rate that clears the international goods market? Show all work

USA

S = 2400 - [420 + .5(2400 - 200) - 300 r ] - 500

S = 380 + 300r

CHINA

S = 2000 - [500 + .5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[380 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-80 + 1000r = 0 .............r* = .08

b) (5 points) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate .

USA

S = 380 + 300(.08) = 404

I = 460 - 200(.08) = 444

NX = -40

CHINA

S = 400 + 300(.08) = 424

I = 400 - 200(.08) = 384

NX = + 40

c) (5 points) Which country is ‘spending beyond its means’ and which country is the saver? What exactly do we mean by the phrase ‘spending beyond its means’ in this context. Be sure to define and use the word absorption in your answer and compare absorption in each country to its income. Explain.

USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y. Absorption in the US is 2440, Y = 2400, Absorption in China is 1960, Y =2000.

Draw two diagrams side by side, with the US on the left and the China on right. Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses.

[pic]

20 points for correct and completely labeled diagrams

We now have a change in conditions: US experiences some economic growth and output rises to 2500. All else remains the same.

d) (10 points) Resolve for the world real interest rate that clears the international goods market along with the ‘new’ Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams. (10 points)

NEW SAVINGS FOR US

S = 2500 - [420 + .5(2500 - 200) - 300 r ] - 500

S = 430 + 300r

[430 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-30 + 1000r = 0 .............r* = .03

USA

S = 430 + 300(.03) = 439

I = 460 - 200(.03) = 454

NX = -15

CHINA

S = 400 + 300(.03) = 409

I = 400 - 200(.03) = 394

NX = +15

e) (5 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means. Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA). Are your results consistent with the US going to AA? Why or why not? Explain and please be specific.

THE US IS HEADED IN THE RIGHT DIRECTION - TRADE DEFICIT FELL FROM 40 TO 15 - STILL A LITTLE WAYS TO GO!

f)(10 points) We know that world output has gone up by 100 and we also know, via the equation below that the world's absorption has to rise by 100 (right hand side of the equation below). Explain where this 100 in additional output was absorbed in each country. Use specific numbers.

Yus + YChina = [C + I + G] US + [C + I + G] China

Real interest rates have fallen by .05... from .08 to .03. As a result, Consumption and Investment in both the US and China will rise.... for the US, C rises by 50 due to the increase in Y (mpc = .5) and rises -300 x -.05 = 15 due to lower r, I in US rises by 10 (-200 x (-.05), Same for China C up by 15, I up by 10- so the fall in r causes absorption to go up by a total of 50 plus the 50 rise in consumption in US due to (induced by) higher income

[pic]

2. (60 points total) We assume that the world consists of two large open economies, USA and China.

USA Initial Conditions

Cd = 400 + 0.5(Y-T) – 300rw

Id = 460 – 200rw

Y = 2400

T = 200

G =500

China Initial Conditions

Cd = 500 + .5(YF – TF) – 300rw

Id = 400 – 200rw

Y = 2000

T = 400

G = 300

a) (10 points) What is the equilibrium interest rate that clears the international goods market? Show all work

USA

S = 2400 - [400 + .5(2400 - 200) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [500 + .5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[400 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-60 + 1000r = 0 .............r* = .06

b) (5 points) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate .

USA

S = 400 + 300(.06) = 418

I = 460 - 200(.06) = 448

NX = -30

CHINA

S = 400 + 300(.06) = 418

I = 400 - 200(.06) = 388

NX = + 30

c) (5 points) Which country is ‘spending beyond its means’ and which country is the saver? What exactly do we mean by the phrase ‘spending beyond its means’ in this context. Be sure to define and use the word absorption in your answer and compare absorption in each country to its income. Explain.

USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y. Absorption in the US is 2430, Y = 2400, Absorption in China is 1970, Y =2000.

Draw two diagrams side by side, with the US on the left and the China on right. Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses.

[pic]

20 points for correct and completely labeled diagrams

We now have a change in conditions: China experiences some economic growth and their output rises to 2100. All else remains the same.

d) (5 points) Resolve for the world real interest rate that clears the international goods market along with the ‘new’ Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams. (10 points)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + .5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 .............r* = .01

USA

S = 400 + 300(.01) = 403

I = 460 - 200(.01) = 458

NX = -55

CHINA

S = 450 + 300(.01) = 453

I = 400 - 200(.01) = 398

NX = +55

e) (5 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means. Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA). Are your results consistent with the US going to AA? Why or why not? Explain and please be specific.

NO , things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55... US has NOT gone to AA.

f)(10 points) We know that world output has gone up by 100 and we also know, via the equation below that the world's absorption has to rise by 100 (right hand side of the equation below). Explain where this 100 in additional output was absorbed in each country. Use specific numbers.

Yus + YChina = [C + I + G] US + [C + I + G] China

Real interest rates have fallen by .05... from .06 to .01. As a result, Consumption and Investment in both the US and China will rise.... for the US, C rises by -300 x -.05 = 15, I in US rises by 10, Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output.. .since mpc = .50 in China, an increase of 100 in Y results in an increase in C by 50. Total increase = 100!

[pic]

3. Suppose we have the following that describes the economy:

IS: Y = 12 – r

MP: r = 1 + .5 π

SRAS: π = πe + γ (Y – YP) + ρ

Given: πe = 2, γ = 1, YP = 10, ρ = 0

What is the equilibrium output, r, and π?

Y = 10, r = 2, π = 2

Now suppose that the IS curve changes and is now:

IS’: Y = 13 – r

What could cause such a change in the IS curve?

Lots of things – check out your notes!

Find the new equilibrium output, r, and π?

Y = 10.66, r = 2.33, π = 2.66

Is this new equilibrium a long-run equilibrium? Why or why not?

NO! Y not equal to YP and π not equal to πe

Now find the long-run equilibrium output, r, and π?

Y = 10, r = 3, and π = 4

4. Suppose we have the following that describes the economy:

IS: Y = 23 – r

MP: r = 2 + .5 π

SRAS: π = πe + γ (Y – YP) + ρ

Given: πe = 6, γ = 2, YP = 18, ρ = 0

What is the equilibrium output, r, and π?

Y = 18, r = 5, π = 6

Now suppose that the IS curve changes and is now:

IS’: Y = 21 – r

What could cause such a change in the IS curve?

Lots of things – check out your notes!

Find the new equilibrium output, r, and π?

Y = 17, r = 4, π = 4

Is this new equilibrium a long-run equilibrium? Why or why not?

NO! Y not equal to YP and π not equal to πe

Now find the long-run equilibrium output, r, and π?

Y = 18, r = 3, π = 2

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