**Economics 102**
**Summer 2011**
**Answers to Homework #5**
**Due 7/13/11**
**Directions: **The homework will be collected in a box **before** the lecture. Please place __your name__, __TA name__ and __section number__ on top of the homework (legibly). Make sure you write your name as it appears on your ID so that you can receive the correct grade. Please remember the section number for the section **you are registered, **because you will need that number when you submit exams and homework. Late homework will not be accepted so make plans ahead of time. **Please show your work.** Good luck!
1. Use the AD/AS model for this question. For each given scenario complete the following four steps:
**Step 1:** Draw the AD/AS model in long-run equilibrium. Label Yfe and the initial price level in this graph. Label all curves and both axes.
**Step 2:** In a second graph model the given event and identify clearly the new short-run equilibrium. This graph should include everything from the first graph as well as the short-run effect of the new event.
**Step 3:** Analyze verbally the short-run status of the economy: 1) is the economy in a boom or a recession?; 2) is unemployment relatively high or relatively low?; and 3) what is happening to the aggregate price level as this economy moves from the long-run position (step 1) to the short-run position (step 2)?
**Step 4:** Draw a graph indicating how this economy will reach long-run equilibrium. Describe verbally this adjustment process.
a. Holding everything else constant, the government increases its level of spending in the economy.
Answer:
Step 1:
Step 2:
Step 3:
This economy is in a boom since Y2 is greater than Yfe. Unemployment is very low due to the boom and the shift in AD to the right has resulted in an increase in the aggregate price level.
Step 4:
Over time wages and prices will be bid up since the economy is operating at a production level greater than Yfe. As nominal wages increase this will cause the SRAS curve to shift to the left from SRAS1 to SRAS2. Eventually the economy will return to Yfe but with a higher aggregate price level than the initial level. Unemployment will return to the full employment or natural rate of unemployment.
b. Holding everything else constant, the government enacts legislation that makes investment spending this year more profitable, and hence, more attractive to businesses.
Answer:
Step 1:
Step 2:
Step 3:
This economy is in a boom since Y2 is greater than Yfe. Unemployment is very low due to the boom and the shift in AD to the right has resulted in an increase in the aggregate price level.
Step 4:
Over time wages and prices will be bid up since the economy is operating at a production level greater than Yfe. As nominal wages increase this will cause the SRAS curve to shift to the left from SRAS1 to SRAS2. Eventually the economy will return to Yfe but with a higher aggregate price level than the initial level. Unemployment will return to the full employment or natural rate of unemployment.
c. Holding everything else constant, the central bank reduces the money supply.
Answer:
Step 1:
Step 2:
Step 3:
This economy is in a recession since Y2 is less than Yfe. Unemployment is very high due to the recession and the shift in AD to the left has resulted in a decrease in the aggregate price level.
Step 4:
Over time wages and prices will decrease since the economy is operating at a production level less than Yfe. As nominal wages decrease this will cause the SRAS curve to shift to the right from SRAS1 to SRAS2. Eventually the economy will return to Yfe but with a lower aggregate price level than the initial level. Unemployment will return to the full employment or natural rate of unemployment.
d. OPEC increases the price of oil at the same time that there is a substantial loss in consumer and business confidence due to a financial crisis in the domestic economy.
Answer:
Step 1:
Step 2:
There are three possible outcomes: Aggregate output will definitely fall relative to its initial level, but the aggregate price level may increase, decrease, or remain the same. See the graphs below for these three possibilities.
Step 3:
This economy is definitely operating in a recession since output has fallen below Yfe. The economy is also experiencing stagflation if the aggregate price level is rising. It is possible for the aggregate price level to be increasing, decreasing, or remaining constant. Due to the recession unemployment is relatively high.
Step 4:
The SRAS supply curve will shift back to the right restoring the economy to full employment level of output. Without more knowledge about the magnitude of the demand shift it is impossible to know with certainty what happens to the aggregate price level in the long-run relative to its initial long-run level.
2. Suppose you are provided the following t-account for the central bank of Macroland and the First Community Bank of Macroland. In Macroland assume that there is only one commercial bank, that this bank will not hold excess reserves and that there are no currency drains (that is, no one in Macroland holds dollars-all transactions are done using checkable deposits).
a. Given the above information, what is the required reserve ratio?
Answer:
Required reserve ratio = [(required reserves)/(demand deposits)]*100 = (200/1000)*100 = 20%
b. Given the above information, what is the money multiplier?
Answer:
Money multiplier = 1/rr = 1/.2 = 5
c. Given the above information, what is the level of the money supply?
Answer:
Money supply = currency in circulation + demand deposits = 0 + 1000 = 1000
d. Holding everything else constant, what happens to the money multiplier when the central bank increases the required reserve ratio? Explain the intuition behind your answer.
Answer:
If the central bank increases the required reserve ratio this results in banks holding more of the demand deposits as reserves instead of using these funds to purchase earning assets (e.g., to make loans). As banks increase their reserves this implies a smaller money multiplier.
e. Suppose the central bank purchases $50 worth of T-bills from First Community Bank. Provide a t-account that illustrates the immediate impact of this purchase on both institutions. Then provide a t-account that illustrates the impact of this transaction on both institutions once full adjustment to this purchase has occurred.
Answer:
Immediate impact:
After full adjustment:
f. After the full adjustment to the event in described in part (e), what is Macroland’s money supply? Verify that the change in the money supply is equal to the money multiplier times the change in reserves.
Answer:
New money supply = 1250
Δ in money supply = new money supply – initial money supply
Δ in money supply = 1250 – 1000 = 250
Δ in money supply = (money multiplier)(Δ in reserves)
Δ in money supply = 5(50) = 250
g. Instead of the scenario described in part (e), suppose the central bank sells $100 worth of T-bills to First Community Bank. Provide a t-account that illustrates the immediate impact of this purchase on both institutions. Then provide a t-account that illustrates the impact of this transaction on both institutions once full adjustment to this purchase has occurred.
Answer:
Immediate impact:
After full adjustment:
h. What is the change in the money supply given part (g)?
Answer:
Δ in money supply = (money multiplier)(change in reserves)
Δ in money supply = 5(-100)
Δ in money supply = -500
When the central bank sells $100 worth of T-bills this causes the money supply in Macroland to decrease by $500.
3. You are given the following information about an economy.
Money supply = Ms = 1000
Money demand = Md = 2000 – 200r where r is the interest rate expressed as a percentage and not a decimal (hence, 2% would be 2 in the equation and not .2)
Required reserve ratio = rr = 20%
There are no currency drains in this economy.
There are no excess reserves in this economy.
Labor demand = Ld: W/P = 20 – (1/1000)Ld where W/P is the real wage and Ld is the quantity of labor demanded
Labor supply = Ls: W/P = (1/1000)Ls where W/P is the real wage and Ls is the quantity of labor supplied
P = aggregate price level = 1 initially
Y = AK^{α}L^{1-α } is the aggregate production function for the economy
^{ }A = 20
K = 100
α = .5
C = 14,900 + .5(Y – T) – 10,000P
TR = 0
G = 200
T = 200
X = 1000
M = 1000
I = (20,000/3) – (1000/3)r
SRAS: Ys = 20,000P where Ys is aggregate supply
AD: Yd = C + I + G + (X – M) where Yd is aggregate demand
a. Start by finding equilibrium in the money market. Use the above information to determine the equilibrium interest rate.
Answer:
In equilibrium in the money market, money supply will equal money demand. Thus, 10 – (1/200)Md = r can be rewritten as 10 – (1/200)(1000) = r. Solving for r we get that the equilibrium interest rate is r = 5%.
b. Now, that you have the equilibrium interest rate calculate the level of investment in this economy when the money market is in equilibrium.
Answer:
I = (20,000/3) – (1000/3)r but r = 5. So, I = (20,000/3) – (1000/3)(5) = 15,000/3 = 5000.
c. What is the full employment level of labor? Find the real wage, W/P, and the nominal wage, W.
Answer:
20 – (1/1000)Ld = (1/1000)Ls and in equilibrium Ld = Ls = Le. Thus,
20 = (2/1000)Le or Le = 10,000
The real wage is $10. The nominal wage is also $10 since the aggregate price level is initially equal to $1.
d. Given the above information and your work in part (c), what is the real wage in this economy?
Answer:
W/P = (1/1000)(10,000) = $10 per unit of labor
e. Find the full employment level of output for this economy.
Answer:
Y = AK^{α}L^{1-α }
Yfe = (20)(10)(100) = 20,000
f. If this economy produces at its full employment level of output, what will labor productivity equal?
Answer:
Y/L = 20,000/10,000 = 2 units of output per unit of labor
g. Given the above information, calculate the aggregate price level for this economy when it is in long run equilibrium.
Answer:
In long run equilibrium LRAS = SRAS = AD. We know from part (e) that the full employment level of output is 20,000 for this economy. We need to calculate the aggregate price level. We can equate the LRAS curve to the SRAS curve and get: Yfe = 20,000P or 20,000 = 20,000P or P = 1. Alternatively we could use the SRAS and AD curves to solve for the aggregate price level. From AD we have Y = C + I + G + (X – M) = 14900 + .5(Y – T) – 10,000P + 5000 + 200 + (1000 – 1000). Simplifying this we get Y = 20,000 + .5Y – 10,000P or Y = 40,000 – 20,000P. Using this expression and the SRAS we get 40,000 – 20,000P = 20,000P or P = 1 when Yfe = 20,000.
h. Suppose the Fed purchases $120 worth of T-bills in the open market. First predict what will happen to the new interest rate (r’), the new money supply (Ms’), the new level of investment (I’), the new short run level of Y (Y’), the new aggregate price level (P’), and the new real wage ((W/P)’) because of this monetary policy. Then, find the new interest rate (r’), the new money supply (Ms’), the new level of investment (I’), the new short run level of Y (Y’), the new aggregate price level (P’), and the new real wage ((W/P)’) because of this monetary policy.
Answer:
Intuitively, the change in monetary policy has expanded the money supply. This should result in lower interest rates, higher investment, greater aggregate demand (the AD curve is shifting to the right), a higher price level, and therefore a lower real wage for a given nominal wage.
This question has many steps in order to get the numeric values.
First step: calculate how the monetary policy affects the money supply.
Change in money supply = (money multiplier)(change in reserves)
Change in money supply = (1/.2)(120)
Change in money supply = 600
New money supply = Ms’ = 1600
Second Step: find the new money market equilibrium since you need to know what the new equilibrium interest rate is.
In equilibrium, Ms = Md
1600 = 2000 – 200r’
200r’ = 400
r’ = 2%
Third Step: Calculate the new value of investment given the new interest rate you found in step 2.
I’ = (20,000/3) – (1000/3)r’
I’ = (20,000/3) – (1000/3)(2)
I’ = 18,000/3 = 6000
Fourth Step: Find the equation that now expresses aggregate demand. Graphically the monetary policy has shifted the AD curve to the right: at every aggregate price level you would see a higher level of aggregate demand.
Yd = C + I + G + (X – M)
Yd = 14,900 + .5(Yd – T) -10,000P + 200 + 6000 + (1000 – 1000)
Yd = 14,900 + .5Yd -.5(200) – 10,000P + 6200
.5Yd = 21,000 – 10,000P
Yd = 42,000 – 20,000P
Fifth Step: Set SRAS equal to the new aggregate demand curve to find the new aggregate price level and the new level of real GDP for this economy.
20,000P = 42,000 – 20,000P
P’ = 1.05
Y’ = 20,000(1.05) = 21,000
Sixth Step: Find the new nominal price given the new aggregate price level you found in step 5.
(W/P)” = 10/1.05 = 9.52
Conclusion, in the short run:
Interest rate decreased
Investment increased
Aggregate output increased
Aggregate price level increased
Nominal wage decreased
i. Discuss the long run adjustment process that will occur as this economy moves from the short-run equilibrium you found in part (h) to the long run equilibrium.
Answer:
In the short run this economy is operating in a boom situation due to the rightward shift of the aggregate demand curve. The economy will adjust in the long run by having nominal wages bid up: this will shift the aggregate supply curve to the left restoring the economy to the full employment level of production but with a higher aggregate price level than the initial level.
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