ECON112 Macroeconomics Problem Set 3 *Solution* Fall 2010 (Instructor: Li, Yao; TA: Fok Pik Lin, Astor) -----------------------------------------------------------------------------------------------------------------------------------Posted: Monday, November 1, 2010 Due: 5:30 PM Monday, November 8, 2010 40 marks total

Part I: True/False/Uncertain Please justify your answer with a short argument for each question and draw a diagram if necessary. (15 marks, 3 marks each: 1 mark for correct judgment and 2 marks for correct argument)

1. Suppose that workers in the Republic of Communia are highly unionized, while workers in the Republic of Individuela are not. In all other respects, the two countries are exactly the same. Then Communia is likely to have a higher natural level of output than Individuela. False. In our model of the labor market, the level of unionization is captured by the

Communia is likely to have a higher natural rate of unemployment than Individuela. Hence Communia is likely to have a lower natural level of output than Individuela.

1

2. Suppose there is a decrease in the price level from P to P’. Given the stock of nominal money, M, this leads to an increase in the real money stock, M/P, which shifts the LM curve down. This implies that the AD curve shifts to the right.

3. When output is below the natural level of output, the actual price level is lower than the expected price level. True. The actual price level equals the expected price level when output is equal to the natural level of output. Because the AS curve is upward-sloping, if output is below its natural level, the actual price level is lower than expected. See diagram:

2

4. In terms of changing output, monetary policy is relatively more effective when the AS curve is relatively flat, while fiscal policy is more effective when the AS curve is relatively steep. False. Monetary and fiscal policies affect the AD curve, not the AS curve. Monetary and fiscal policies...

...ProblemSet3
Macroeconomics, ECON 2123
Sections L3 and L4 P. Sen
Posted 9.11.14.
Due 5 PM 17.11.14.
-----------------------------------------------------------------------------------------------------------------------------------
100 marks total
Part I: True/False/Uncertain Please justify your answer with a short argument for each
question and draw a diagram if necessary. (25 marks, 5 marks each: 2 marks for correct
judgment and3 marks for correct argument)
1. Suppose that workers in the Republic of Communia are highly unionized, while workers
in the Republic of Individuela are not. In all other respects, the two countries are exactly
the same. Then Communia is likely to have a higher natural level of output than Individuela.
2. Suppose there is a decrease in the price level from P to P’. Given the stock of nominal
money, M, this leads to an increase in the real money stock, M/P, which shifts the LM curve
down. This implies that the AD curve shifts to the right.
3. When output is below the natural level of output, the actual price level is lower than the
expected price level.
4. In terms of changing output, monetary policy is relatively more effective when the AS
curve is relatively flat, while fiscal policy is more effective when the AS curve is relatively
steep.
5. The aggregate demand relation slopes down because at a higher price level, consumers
wish to purchase fewer goods.
Part II: The...

...Problemset3 (Answer)
7.6. A farmer uses three inputs to produce vegetables: land, capital, and labor. The production function for the farm exhibits diminishing marginal rate of technical substitution.
a) In the short run the amount of land is fixed. Suppose the prices of capital and labor both increase by 5 percent. What happens to the cost-minimizing quantities of labor and capital for a given output level? Remember that there are three inputs, one of which is fixed.
b) Suppose only the cost of labor goes up by 5 percent. What happens to the cost-minimizing quantity of labor and capital in the short run.
a) The amount of land used in production is fixed in the short-run. Hence, in the short-run the farmer chooses amount of capital and labor. It follows that cost-minimizing quantities of labor and capital have to satisfy equation MPL / MPK = w/r where w and r denote prices of labor and capital. Notice that w/r = (1.05 w)/ (1.05 r). The cost-minimizing quantities of inputs, for each level of output, do not change when prices of both inputs go up by 5% and quantity of land is fixed.
b) For a given output level, the cost-minimizing farmer uses more capital and less labor.
7.9. Suppose the production of airframes is characterized by a Cobb–Douglas production function: Q = LK. The marginal products for this production function are MPL = K and MPK = L. Suppose the price of labor is $10 per unit and the price of capital is $1...

...Department of Economics University of California, Berkeley
Fall 2012 Econ 182
SolutionsProblemSet 8
Problem 1. Exchange Rates and International Transmission a. Suppose that the US engages in a monetary expansion. Since exchange rate is pegged to the US dollar, country X’s monetary authorities are forced to expand their money supply as well (recall that i = i* under FixER). Interest rates fall in country X, output expands, and of course the exchange rate remains unchanged. On the AA-DD diagram, both the AA and the DD schedules shift to the right. The shift in DD can be explained by the increase in US output which causes an increase in net exports of country X. In addition, smaller interest rates are known to increase investment, which can also explain the shift in DD. The case of monetary contraction is similar. Thus with fixed exchange rates, monetary shocks transmit positively from the US to country X.
b. Suppose now that the US aggregate demand increases. Perhaps fiscal policy in the US expands. An increase in the US aggregate demand increases US nominal rates and, with fixed exchange rates, forces monetary authorities in country X to contract the money supply (in order to keep i = i*). Monetary contraction in country X leads to a fall in output due to a decline in investment. Exchange rate of course is unchanged. In the AA-DD diagram, both AA and DD schedules shift to the left. The reverse argument...

...ECON 213
PROBLEMSET3
Name: ___Krystal Logsdon_____________________________________
ProblemSet3 is to be completed by 11:59 p.m. (ET) on Monday of Module/Week 6.
1. Data for the market for graham crackers is shown below. Calculate the elasticity of
demand between the following prices.
Price of
crackers
Quantity Demanded (per month)
$3
80
$2.5
120
$2
160
$1.5
200
$1
240
$1.00 - $1.50: __*_-0.333__________________________
$1.50 - $2.00: __*__-0.6___________________________
$2.00 - $2.50: ___*_-1_____________________________
$2.50 - $3.00: __*___-1.66_________________________
If the price of graham crackers is $2.50 should firms raise or lower their prices if they
want to increase revenue? Explain this in terms of elasticity.
*The firm should lower their prices. The elasticity of demand increases.
Page !1 of !4
ECON 213
2. Assume the competitive market shown below faces a short run price of $10. Using
the graph below, identify the following:
Profit maximizing output:
*_MC=MR___Q=110________
Approximate mark up over cost ___*__There would be no mark up over cost___
In the long run, the price falls to $7.50. Why does this happen?
*The business operates at the minimum average total cost (ATC), which at $7.50 is equal
to the marginal cost.
Price, Cost
What is the new profit maximizing output? _*_Minimum Average Total Cost
(ATC)____Q=90_________________...

...ProblemSet3
Name: Lauren Hensley
ProblemSet3 is to be completed by 11:59 p.m. (ET) on Monday of Module/Week 6.
1. Data for the market for graham crackers is shown below. Calculate the elasticity of demand between the following prices.
Price of crackers
Quantity Demanded (per month)
$3
80
$2.5
120
$2
160
$1.5
200
$1
240
$1.00 - $1.50: -0.333
$1.50 - $2.00: -0.6
$2.00 - $2.50: -1
$2.50 - $3.00: -1.66
If the price of graham crackers is $2.50 should firms raise or lower their prices if they want to increase revenue? Explain this in terms of elasticity.
The firm should lower the price as we see the elasticity increases
2. Assume the competitive market shown below faces a short run price of $10. Using the graph below, identify the following:
Profit maximizing output: MC=MR, Q=110
Approximate mark up over cost There is no mark up
In the long run, the price falls to $7.50. Why does this happen? Ther are no fixed costs and the firm operates at minimum ATC which is equal to marginal cost
What is the new profit maximizing output? Min ATC, Q=90
3. A local hardware store is trying to decide whether to stay open. They have found that their industry is extremely competitive and profits have shrunk considerably. Knowing that you have taken an economics course the owners have asked for your opinion. Draw a...

...ProblemSet3ProblemSet3 is to be completed by 11:59 p.m. (ET) on Monday of Module/Week 6.
1. Data for the market for graham crackers is shown below. Calculate the elasticity of demand between the following prices.
Price of crackers
Quantity Demanded (per month)
$3
80
$2.5
120
$2
160
$1.5
200
$1
240
$1.00 - $1.50: Elasticity of demand equals .45; favoring inelasticity
$1.50 - $2.00: Elasticity of demand equals .78; favoring inelasticity
$2.00 - $2.50: Elasticity of demand equals 1.29; favoring elasticity
$2.50 - $3.00: Elasticity of demand equals 2.2; favoring elasticity
If the price of graham crackers is $2.50 should firms raise or lower their prices if they want to increase revenue? Explain this in terms of elasticity.
The firm should lower their prices 50 cents in an attempt to raise revenues. The elasticity of demand from 2.50-2.00 is 1.29, meaning with a reduction in prices there would be an elastic effect on quantity demanded. The maximum profit would be reached at the price of $2 because of the increased in demand with the price reduction.
2. Assume the competitive market shown below faces a short run price of $10. Using the graph below, identify the following:
Profit maximizing output: 110
Approximate mark up over cost: $2 per unit
In the long run, the price falls to $7.50. Why does this happen?
An increase in demand would temporarily increase the...

...ProblemSet3
Name
ProblemSet3 is to be completed by 11:59 p.m. (ET) on Monday of Module/Week 6.
1. Data for the market for graham crackers is shown below. Calculate the elasticity of demand between the following prices.
Price of crackers
Quantity Demanded (per month)
$3
80
$2.5
120
$2
160
$1.5
200
$1
240
$1.00 - $1.50: ___$-0.45________________________________
$1.50 - $2.00: ____$_-0.77______________________________
$2.00 - $2.50: _____$_-1.28_____________________________
$2.50 - $3.00: ____$_-2.22______________________________
If the price of graham crackers is $2.50 should firms raise or lower their prices if they want to increase revenue? Explain this in terms of elasticity.
Since the elasticity increases, the price would be lower
2. Assume the competitive market shown below faces a short run price of $10. Using the graph below, identify the following:
Profit maximizing output: _110___________________
Approximate mark up over cost __$2.50_____________________
In the long run, the price falls to $7.50. Why does this happen?
The demand increased, since they can produce more at a lower price
What is the new profit maximizing output? ______90_________________
3. A local hardware store is trying to decide whether to stay open. They have found that their industry is extremely competitive and profits have shrunk considerably. Knowing that you...

...SOLUTIONS
Financial Management
Seminar + Homework, Week 5
1. Starware Software was founded last year to develop software for gaming applications. Initially, the founder invested $800,000 and received 8 million shares of stock. Starware now needs to raise a second round of capital, and it has identified an interested venture capitalist. This venture capitalist will invest $1 million and wants to own 20% of the company after the investment is completed.
a. How many shares must the venture capitalist receive to end up with 20% of the company? What is the implied price per share of this funding round?
b. What will the value of the whole firm be after this investment (the post-money valuation)?
Answer:
a. After the funding round, the founder’s 8 million shares will represent 80% ownership of the firm. To solve for the new total number of shares (TOTAL):
8,000,000 = 0.80 TOTAL
So TOTAL = 10,000,000 shares. If the new total is 10 million shares, and the venture capitalist will end up with 20%, then the venture capitalist must buy 2 million shares. Given the investment of $1 million for 2 million shares, the implied price per share is $0.50.
b. After this investment, there will be 10 million shares outstanding, with a price of $0.50 per share, so the post-money valuation is $5 million.
2. Three years ago, you founded your own company. You invested $100,000 of your money and received 5 million shares of Series A preferred stock. Since then, your company has...