Economics

Economics
Question 1 (35 points) – Chapters 6, 10 & 11
Fantasy Island is a closed economy and is characterized by the following equations:
Consumption: C = 400 + 0.75(Y – T)
Investment: I = 150 – 1500r
Government spending: G = 350
Taxes: T = 400
Real money demand: L = 0.4Y – 2550i, where i = r + ?e
Expected inflation: ?e = 0
Production function: Y = K1/2L1/2
The nominal money supply = 630
Note: Interest rates, i and r, are expressed in decimal points, i.e., if r = 0.5, then r = 50%.

Suppose the IS-LM model can be to describe Fantasy Island, and answer the following questions. Keep your answer to TWO decimal points if necessary.

a) Derive the IS and LM equations for this economy. (4 points)

b) Suppose, in the long-run, 2000 (real) units of capital are utilized and 2000 workers are employed. Calculate the resulting full-employment values of real output, real interest rate, investment, consumption, the government budget balance, and the price level. (6 points)

c) Suppose the economy is initially in its long-run equilibrium as shown in part B above. Now,autonomous consumption suddenly (and permanently) falls by 5%. Calculate the resulting (new) short-run equilibrium values of real output, real interest rate, investment, consumption, and the real money supply. Determine the unemployment rate that results in short-run equilibrium. (6 points)

d) Suppose, as well, we are also told that when the economy was in long-run equilibrium in part B (above), 120 people were unemployed. Further, when the shock hit the economy (in part C, above) in net terms no people have exited/entered the labour force. In light of this new information determine the unemployment rate that results in the short-run equilibrium from part C. What portion this unemployment is represented by cyclical unemployment and what portion is comprised of those in the natural rate (level of) unemployment (NRU). (4 points)

Hint: Cyclical unemployment is the level of unemployment that results from deviations of output from the full-employment level.

e) When the economy returns to long-run equilibrium what unemployment rate should we expect to see? Explain why/when this makes sense. (4 points)

f) Determine the (new) LR equilibrium values of real output, real interest rate, investment, consumption, and the real money supply that result due to the shock described in part C (above). (6 points)

g) Draw one well labeled IS/LM diagram that depicts the initial LR, the new SR and new LR equilibria for this economy. (5 points)

Question 2 (30 points) – Chapters 10 & 11
The closed economy of Krashinskystan is experiencing a debate about the strength and appropriateness of certain government policies. Significant debate is occurring among different groups within the country. The economy is presently in long-run equilibrium and the government has decided that it is sensible to raise the level of taxes it charges (as they feel they do not collect “enough” taxes presently). The debate is raging as to what mix of fiscal (tax and/or spending) and monetary policy would be most effective at ensuring unemployment is not too highin the short-run. The debate also centers on what policy mix is most sensible for the economy in the short- and long-run.

The three policy mixes being considered are as follows:
1) Increase T and use all of this additional revenue to reduce government borrowing (i.e. reduce bond sales).
2) Increase T and use all of this additional revenue to increase government spending on goods & services.
3) Increase T and send all of this additional revenue to the central bank as cash to be permanently taken out of circulation (i.e. to be destroyed).

a) Which of the three policy mixes is most effective at keeping unemployment from fluctuating significantly in the short-run? Explain, using words and a single IS/LM diagram, the degree of effectiveness of each of the three policy mixes. (15 points)

b) What effect does each policy mix have on the government budgetary position or balance? Why might this matter to the government? What (other) longer term considerations might the government consider besides its budgetary balance? Explain. (15 points)

 
Question 3 (35 points) – Chapter 5
Suppose the small open economy Iceland has perfect financial capital mobility and no risk premium. Some of their information is:

C = 150 + 0.60(Y – T) – 25r

I = 200 – 75r

Note: Here r is measured in decimal point form, so that r = 0.02 represents a real interest rate of 2 percent).

a) Derive an expression for long-run equilibrium in this economy in terms of net exports (NX), using the above information. (5 points)

b) Now suppose the long-run level of output is 1000, government spending on goods and services is equal to 100 and the government budget is balanced, and the world real rate of interest is equal to 5 per cent. Determine the level of net exports for Iceland. Is the country a net saver internationally? What is the (net) level of saving in Iceland coming from the rest of the world? (6 points)

c) What would happen to net exports (NX) if there was a deterioration of the government budget balance of 10 which was the result of:
i) An increase in G; or
ii) A reduction in taxes?
If the results are different, explain why. (8 points)

d) Suppose in addition to the deterioration in the government budget balance, described in part B above, we are told that this was caused by a tax cut and in response international investors have grown concerned about the prospects for the Icelandic economy. As a result international investors demand a 2 percentage point risk premium on loans made to borrowers in Iceland. Determine the resulting long-run equilibrium levels of real output, real interest rate, investment, consumption, and net exports. (8 points)

Hint: Think about what, if anything happens to the real interest rate faced by Iceland. You may need to find the new level of the interest rate before answering this question.

e) Draw two diagrams depicting long-run equilibrium, one for the domestic loanable funds market in Iceland and one for the foreign exchange market. In each diagram clearly label the initial long-run equilibrium from part A & the new long-run equilibrium from part D. Has the domestic currency (DC) experienced a real appreciation or depreciation? Be sure to provide a short written explanation of your findings.(8 points)

 
ECMB05 – Macroeconomic Theory and Policy
Sample Assignment 2: SOLUTIONS
Question1 – Chapters 6, 10 & 11 – 35 Marks (4, 6, 6, 4, 4, 6, and 5 marks respectively)

Part A) (4 marks)
• IS curve is given by goods market equilibrium:
Y= C + I + G
Y = [400 + 0.75(Y – 400)] + [150 – 1500r] + 350
Y = 600 + 0.75Y– 1500r
Y = 2,400 – 6,000r OR r = 0.4000 – 0.0001667Y (2 marks)
• LM curve is given by money market equilibrium:
MS/P = L(i, Y) = L(r + ?e, Y)
630/P = 0.4Y – 2550r
2550r = 0.4Y – (630/P) or 0.4Y = (630/P) + 2550r
r = 0.000156862Y – (0.247058823/P) Y= (1,575/P) + 6,375r (2 marks)

Part B) (6 marks)
• Output, Y:
Y= YFE = 2,000 = (2000)0.5(2000)0.5 (1 mark)
• Real interest rate r:
In the long run, we can find the real interest rate from the IS curve (i.e. at IS = FE).
Y = 2400 – 6000r
2000 = 2400 – 6000r
6000r = 400
r = 0.0667 (6.67%) (1 mark)
• Price level, P:
In the long run we can find the price level from the LM curve (i.e. at LM = IS = FE)
Y= 1575/P + 6375r
2000 = (1575/P) + 6375(0.06667)
(1575/P) = 1575
P = 1.00 (1 mark)
• Investment, I:
In equilibrium I = 150 – 1500(0.06667) = 50 (1 mark)
• Consumption, C:
In equilibrium C = 400 + 0.75(2000 – 400) = 1,600 (1 mark)
• Government budget balance, SGOVT:
In equilibrium SGOVT = T – G = 400 – 350 = 50 (1 mark)

Part C) (6 marks)
Now, suppose C0 decreases to shift the Cons function to C = 380 + 0.75(Y – T)
• The new IS curve:
Y= C + I + G
Y = [380 + 0.75(Y – 400)] + [150 – 1500r] + 350
Y = 580 + 0.75Y– 1500r
Y = 2,320 – 6,000r OR r = 0.38666667 – 0.0001667Y
• Short run equilibrium values:
? Price level, P:
P = 1.00 (because P is held fixed in the short run)
? Real interest rate, r:
Equate IS to LM:
2320 – 6000r = (1575/1.00) + 6375r
12375r = 745
r = 0.0602 (6.02%) (1 mark)
? Output, Y:
Sub r = 0.0602 into the IS curve or LM curve:
IS curve: LM curve:
Y = 2320 – 6000r Y = (1575/1.00) + 6375r
Y = 2320 – 6000(0.0602) Y= 1575 + 6375(0.0602)
Y = 1,958.80 Y = 1,958.78 (1 mark)
Note: The answer above keeps r at 0.0602. If you sub r = 0.0602 into the IS equation, your answer should be 1,958.80. If you sub r = 0.0602 into the LM equation, your answer will be 1,958.775. Both answers are accepted and the difference is due to a rounding problem.

? Investment, I: I = 150 – 1500(0.0602) = 59.70 (1 mark)

? Consumption, C: C = 400 + 0.75(1958.80 – 400) = 1,549.09 (0.5 mark)

? Real money supply, (M/P): (MS/P) = (M/P) = 630 (0.5 mark)

? Unemployment Rate, UR:

SR employment = LSR = ( YSR* )2/K = (1958.80)2/2000 = 1918.45 = E
Labour force = LF = 2000 = E + U
Unemployed = U = (LF – E) = 81.55

Unemployment rate = UR = (U/LF) = (81.55/2000) = 0.0408 or 4.08% (2 marks)

Part D) (4 marks)
Here the information provided yields
? Unemployment Rate, UR:

SR employment = LSR = ( YSR* )2/K = (1958.80)2/2000 = 1918.45 = E
Labour force = LF = 2120 = E + U
Unemployed = U = (LF – E) = 201.55

Unemployment rate = UR = (U/LF) = (201.55/2120) = 0.0951 or 9.51% (2 marks)

 

In LR equilibrium, 120 people where (are) unemployed. Therefore, with 201.55 people unemployed in our SR equilibrium 81.55 of these are the cyclically unemployed (these people have become unemployed due to the SR business cycle driving the economy away from LR equilibrium). So as a fraction of the total number of unemployed people approximately 40% of the pool of unemployed people is comprised of people who are cyclically unemployed (i.e. unemployed for cyclical reasons) and about 60% are in the NRU pool (i.e. are unemployed due to LR economic reasons). (2 marks)

Part E) (4 marks)
In long-run equilibrium
? Unemployment Rate, UR:

SR employment = LSR = ( YSR* )2/K = (2000)2/2000 = 2000 = E
Labour force = LF = 2120 = E + U
Unemployed = U = (LF – E) = 120

Unemployment rate = = (120/2120) = 0.0566 or 5.66% (2 marks)

 

In LR equilibrium, 120 people will be unemployed. Therefore, with 120 people unemployed in our new LR/SR equilibrium none of these are the cyclically unemployed (as in LR equilibrium no one can claim to be unemployed due to the SR business cycle driving the economy away from LR equilibrium). So as a fraction of the total number of unemployed people 0% of the pool of unemployed people is comprised of people who are cyclically unemployed (i.e. unemployed for cyclical reasons) and 100% are in the NRU pool (i.e. are unemployed due to LR economic reasons). (2 marks)

Part F) (6 marks)
In long-run equilibrium
• Output, Y:
Y= YFE = 2,000 = (2000)0.5(2000)0.5 (1 mark)
• Real interest rate r:
In the long run, we can find the real interest rate from the IS curve (i.e. at IS = FE).
Y = 2320 – 6000r
2000 = 2320 – 6000r
6000r = 320
r = 0.0533 (5.33%) (1 mark)
• Price level, P:
In the long run we can find the price level from the LM curve (i.e. at LM = IS = FE)
Y= 1575/P + 6375r
2000 = (1575/P) + 6375(0.0533333)
(1575/P) = 1660
P = 0.9488
• Investment, I:
In equilibrium I = 150 – 1500(0.053333) = 70 (1 mark)
• Consumption, C:
In equilibrium C = 380 + 0.75(2000 – 400) = 1,580 (1 mark)
• Real money supply, (M/P):
In equilibrium (MS/P) = (M/P) = 664 (2 marks)

Part G) (5 marks)
Diagram (5 marks: must be fully labeled (all axis, curves, shifts, equilibria) for full marks)
Where:

Point A = Initial LR equilibrium

Point B = New SR equilibrium (following the shock)

Point C = New LR equilibrium (following the shock)

Question 2 – Chapter 10/11 – 30 Marks (15 and 15 marks)

Part A) (15 marks)

• Policy Mix #1: The tax increase shifts the IS curve down to the right to IS1 no change has occurred to cause further shifts to either the IS or LM curves. So the economy settles into a new SR equilibrium at the intersection LM0 = IS1 which lowers Y to Y1. (2 marks)
• Policy Mix #2: The tax increase shifts the IS curve down to the right to IS1 while the increase in government spending on goods and services shifts the IS curve up towards the right. Since the spending multiplier is one unit larger than the tax multiplier in absolute value the rightward IS shift is larger than the leftward IS shift. No change has occurred to shift the LM curve. So the economy settles into a new SR equilibrium at the intersection LM0 = IS2 which raises Y to Y2. Note: The net increase in Y is smaller than the net decrease in Y experienced with policy mix #1. (2 marks)
• Policy Mix #3: The tax increase shifts the IS curve down to the right to IS1 and the destruction of the money raised by the new taxes shifts the LM curve up towards the left to LM1. So the economy settles into a new SR equilibrium at the intersection LM1 = IS1 which lowers Y to Y3. Note: Due to the second shift the decrease in Y is larger than the decrease in Y experienced with policy mix #1. (2 marks)
• SR goal: Keep unemployment from fluctuating significantly. This is achieved by keeping output (Y) from fluctuating significantly in the SR (since physical capital (K) and technology (A) are fixed in the SR). (2 marks)
• The policy mix that is most effective at keeping unemployment from fluctuating significantly in the SR is policy mix #2 – raise taxes & use this additional revenue to increase government spending on goods & services. We can clearly see this as this policy (mix) results in the smallest net fluctuation in real output – this implies it results in the smallest net fluctuation in unemployment. (2 marks)

• Diagram (5 marks)

Part B) (15 maks)
Impact to government budgetary position:
• Policy Mix #1: The tax increase raises government savings (SG = T – G, so ?SG = ?T > 0). The larger the tax increase the larger the improvement in the governments’ LR budgetary position. (3 marks)
• Policy Mix #2: The tax increase coupled with an increase in government spending on goods and services of the same size has NO impact on government savings (SNAT = T – G, so ?SG= ?T – ?G = 0 since ?T = ?G). This policy mix neither improves nor harms the governments’ LR budgetary position. (3 marks)
• Policy Mix #3: The tax increase coupled with the destruction of the money raised by the new taxes raises government savings (SG = T – G, so ?SG = ?T > 0). The larger the tax increase the larger the improvement in the governments’ LR budgetary position. (i.e. the destruction of some nominal money has no lasting effects in the LR, since money does not impact real variables in the LR, it is neutral according to the Classical dichotomy). (3 marks)
• The budgetary balance matters to the government since a (large) negative balance would cause the level of government debt to rise higher and higher over time. If the budgetary balance is too negative people, investors and citizens alike, might feel the (growing) amount of outstanding government debt is unsustainable. If the debt grows too high this might lead investors to not want to hold the debt (bonds) of the domestic government fearing that the finances of the government are not sufficient to pay their debts in the future – say, like in the case of Greece. This can result in a risk premium being demanded by investors. (2 marks)

Other longer-term considerations: (4 marks for any two good arguments – such as below)
• Price stability & Inflation: Over the longer term the government might be concerned with the stability of the price level (and the inflation rate) as large price changes can harm some individuals.
• Appropriate fiscal policy mix: The government might care that the mix of tax and spending is appropriate to support a good business environment in the longer term that is supportive of longer term growth.
• Achieving a “good” real interest rate level: The government might care about obtaining a “good” level for the real interest rate (you should recall they can influence this since the economy is closed). A low level of the real interest rate would raise the level of investment which in the very long-run can lead to greater accumulation of physical capital (i.e. the growth rate of K would rise) which would increase the rate of growth of real GDP (i.e. think of the growth accounting formula).

 

Question 3 – Chapter 5 – 35 Marks (5, 6, 8, 8, and 8 marks respectively)

Part A) (5 marks)
• First derive an expression for national saving, which is:
S = Y – C – G
S = Y – [150 + 0.60(Y – T) – 25r] – G
S = 0.40Y – 150 + 0.60T + 25r – G
• The national income identity is:
Y = C + I + G + NX
Y – C – G = I + NX
S = I + NX
NX = NFI = S – I

NX = 0.40Y – 150 + 0.60T + 25r – G – 200 + 75r

NX = 0.40Y + 0.60T + 100r – (350+G) (5 marks)

Part B) (6 marks)
• Given: Y = 1000, G = 100 = T, r = 0.05
• NX = 0.40(1000) + 0.60(100) + 100(0.05) – (350+100)
NX = 400 + 60 + 5 – 450
NX = 15 (2 marks)
• Since NX is positive this means that Iceland is a net saver internationally. Since Iceland is running a trade surplus this means they are net lenders to the ROW (the rest of the world). (2 marks)
• The net level of saving coming from the ROW is equal to:
SROW = NFI = 15 (2 marks)
Part C) (8 marks)
Now, suppose SG = (T – G) decreases by 10
• Case 1: This was the result of an increase in G:
?NX = – ?G = – ( 10 ) = – 10
Net exports (NX) would decline by 10 (to NX = 5). (2 marks)
The world real rate of interest is unchanged (due to this shock).
• Case 2: This was the result of a reduction in taxes T:
?NX = ?S = 0.60(?T) = 0.60( -10 ) = – 6
Net exports (NX) would decline by 6 (to NX = 9). (2 marks)
The world real rate of interest is unchanged (due to this shock).
• NX changes one-to-one with the change in G. (2 marks)
• NX changes less than one-to-one with the change in T (since a portion of the tax cut would be saved). Since net exports (NX) is the difference between saving and investment the deterioration of the trade balance (NX) is smaller in the tax cut case than in the case of an increase in G. (2 marks)

Part D) (8 marks)
• Output, Y:
This has no impact on inputs or technology (in the LR). So Y = 1,000 (unchanged). (1 mark)
• Real interest rate, r:
r = rW + ? = 0.05 + 0.02 = 0.07 or 7% (rose 2 percentage points) (1 mark)
• Investment, I:
I = 194.75 (I fell, ?I = – 75?r = – 75(0.02) = – 1.5) (2 marks)
• Consumption, C:
C = 694.25 (C fell, ?C = – 25?r = – 25(0.02) = – 0.5) (2 marks)
• Net exports, NX:
NX = S – I = 11 (NX rose, ?NX = ?S – ?I = 0.5 – (-1.5) = 2) (2 marks)

Part E) (8 marks)
Diagram (4 marks – 2 marks each diagram)
In the initial LR equilibrium (from parts A & B) Iceland has a trade surplus of 15 since at the world real interest rate national saving exceeds investment.

When taxes are cut government saving falls by more than private saving rises (a portion of the tax cut is saved). So national saving shifts up to the left. This lowers NX at the world real rate of interest (?NX = ?S < 0, but NX is still positive following this shock in part C). The decrease in the government budget balance causes investors to impose a risk premium on investment in Iceland (in part D). This drives up the domestic real rate of interest (?r = ?? = 0.02 = 2%) this crowds out some domestic investment which has the effect of raising net exports some back towards its initial (part A&B) level (as ?NX = ?S-?I). (2 marks)

The two shifts the shock in part D causes both have the effect of driving the real exchange rate up. That is, the shock(s) cause the domestic Icelandic currency to experience a real appreciation (versus foreign currencies). (2 marks)

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