Practice Calculations I For Questions

Practice Calculations

I for questions #1 -- 4, show how you set up each step of the problem. it's not acceptable just to show a correct numeric answer if the method for solving is not shown.

The following equations describe monthly demand and supply for office cleaning services:

2000 + 15P -- L

where QD = quantity demanded, P = price, I = disposable income per household, QS = quantity supplied, and L = license the seller must purchase in order to do business.

If disposable income (i) per household is $4,400 and the seller's license cost (L) is $20,

Write the equation of the demand curve in terms of price and quantity (that is, price and quantity should be the only "variables").

Substitute i:

QD = 5000 -- 10P + (6)(4400)

QD = 31400 -- 10P

Write the equation of the supply curve in terms of price and quantity.

Substitute L: Qs = -2000 + 15P --

Qs = 15P - 2020

c.

At what price would demand equal zero?

To calculate this, substitute 0 for the demand:

0 = 31400 -- 10(P)

-31400 = -10P

divided by -10

3140 = P

d. At what price would supply equal zero?

Substitute 0 for Qs

0 = 15P -- 2020

2020 = 15P

divide by 15

P = 134.67

e.

What is the equilibrium price?

The equilibrium price is where Qd and Qs are equal:

31400 -- 10P = 15P -- 2020

33420 = 25P

P = 1336.8

f.

What is the equilibrium level of output?

For this, we use the Qs formula:

Qs = 15 (1336.8) -- 2020

g.

Plot the supply and demand curves on a graph. Clearly show equilibrium on the graph.

h.h. Suppose the license fee is eliminated; suppliers are not required to purchase a license (that is, the license fee is zero). Write the equation of the new supply curve.

Qs = 15P - 2000

What is the new equilibrium price using the new supply curve in part "h" and the original demand curve?

31400 -10P = 15P -- 2000

33400 = 25P

P = 1336

j.

What is the new equilibrium quantity using the new supply curve in part "h" and the original demand curve?

Qs = 15P -- 2000

Qs = (15)(1336) -- 2000

Qs = 18040

k. Use the original equilibrium information in parts "e" and "f" and the new equilibrium information in parts "I" and "j" to calculate the price elasticity of demand in this range.

Price elasticity of demand is the percentage change in demand for a change in price.

Thus: Qd / ?Qs. This can be rewritten as:

Qdnew -- Qdold / Pnew -- Pold or (18040 -- 18032) / 18032 / (1336 -- 1336.8) / 1336.8

.0004436 / -.0005984 = -0.74

The elasticity of demand is -0.74

l.

Based on your answer to part "k" is demand elastic?

0.74 is not usually considered to be elastic. The boundary for elasticity is 1.0, so if a slope is above 1.0 then demand is considered to be elastic; below 1.0 is not elastic.

m. Suppose that you run a company that provides services in this market. Currently, you supply 2000 cleaning contracts per month (other firms supply the rest). What is your total revenue using the price you determined in part "e"?

n. Again suppose that you run a company that provides services in this market. Currently, you supply 2000 cleaning contracts per month (other firms supply the rest). What is your total revenue using the price you determined in part "i"?

Revenue = Q * P = 2000 * 1336.8 = $2,673,600

o. Did total revenue increase, or did it decrease, when price changed from the price in part "e" to the price in part "f"?

The price did not change in part f. Part f asked to calculate the equilibrium level of output give the price in part e. If the question refers to the new equilibrium price from "i" then the answer is as follows:

Revenue = Q * P = 2000 * 1336 = $2,672,000, or a difference of $-1600.

p. Is the change in total revenue that you describe in part "o" what you would expect based on the elasticity you describe in part "l"? (Hint: It should be. If it's not, go back and find the mistake.)

The change is consistent with expectations. Following the questions, Q (sales) did not change while the price went down. Thus, revenue would be expected to fall. The company should have lowered its price in response to a lower equilibrium price. By holding its prices, it effectively lost sales (it did not benefit from the increase in total market volume when P. decreased).

q. Given the current situation in this market, would you be more likely to increase your price, decrease your price, or keep your price the same? Why?

Given the current situation in the market, the firm should lower its price. The equilibrium price has decreased, so the response from the company should be to lower its prices in response. This will help it maintain its market share -- it is currently priced higher than competitors.

2. a) I am not sure that this is a good model equation. The issue here is monthly demand, not total demand. It has to be considered whether or not there will be repeat buyers, and what the total market size might be, because monthly sales are not going to be one-time in nature, not recurring. To change, I would incorporate some estimate of the total market demand -- the price of computers is listed by the demand for computers is not explicitly listed. Another issue is that if a person spends more on a computer system, he/she might be more likely to purchase this device. Right now the formula assumes less likely. To correct this, I would replace the negative with a positive in front of the 100Px.

b)

What would projected QD be if Electronic Innovations were to charge a price of $100 for the module and values of the independent variables next year are expected to be as follows:

i = average annual income = $50,000

PX = price of the computer system that the module would attach to = $1,500

S = shipping cost of the module = $25

Qd = 60,000 -- (500) [HIDDEN] + (5)(50,000) -- (100)(1500) -- (.1)(25)

Qd = 60,000 -- 50,000 + 250,000 -- 150,000 -- 2.5

Qd = 109,997.5

c.

What would projected QD be if Electronic Innovations were to charge a price of $125 for the module and values of the independent variables were the same as in part "b"? Should they consider charging the higher price? Why or why not?

Qd = 60,000 -- (500) [HIDDEN] + 250,000 -- 150,000 -- 2.5

Qd = 97,497.50

To determine if they should charge the higher price, calculate revenues at each price level:

Revenue1 = 109,997.5 * 100 = $10,999,750

Revenue2 = 97,497.5 * 125 = $12,187,187

The company should sell at the higher price, as it will see higher revenues as a result.

3)

Consider a firm that has just rented space and equipment, and started hiring workers to provide consulting services. No variable materials other than labor are needed.

For parts 3a -- 3g, use the table at the bottom of the page:

a.

Fill in Column (a) in the table.

The formula is: Additional output / addition labor so for 20 workers you have:

(900 -- 400) / (20 -- 10) = 50

b.

Fill in columns (b) and (c) in the table assuming that the firm expects to sell the product for a price of $33.

For b) the formula is a * 33

For c) the formula is

c.

If each worker earns $250.00 per day, how many workers should the firm hire?

The firm should hire 60 workers, because at 70 workers, the marginal product of workers is below $250, which is the marginal cost of a new worker.

d.

Fill in the total labor cost in column d if each worker earns $250/day.

e.

Fill in the total cost in column e if the space is rented for $20,000/day.

f.

In order to maximize profits or minimize losses, how much should the firm produce according to the Marginal Revenue/Marginal Cost rule?

The marginal cost formula is: Increase in Total Cost/Increase in workers

The firm should produce at the point where marginal revenue exceeds marginal cost. Thus the firm should hire 60 workers and produce an output of 1900 per day. This gives a profit of $27,700. After this point, the profit begins to decrease.

g.

At the amount you indicated in part f, how much is the firm's profit or loss? Will the firm continue to stay in this industry if the situation stays the same?

At this point, output is 1900 so profit equals:

(1900 * 33) -- (20,000 + (60*250)), or:

$62,700 - $35,000 = $27,700

Number of Workers

Output

(a)

Marginal Product (of Labor)

(b)

Marginal

Revenue Product

(c)

Total

Revenue

Fixed

Cost

(d)

Total (Variable)

Labor

Cost

(e)

Total

Cost

(f)

Marginal

Cost

0

0

20,000

10

40

13200

20,000

22500

20

50

29700

20,000

25000

30

40

42900

20,000

27500

40

30

52800

20,000

10000

30000

50

20

59400

20,000

12500

32500

60

1900

10

62700

20,000

15000

35000

70

1950

5

64350

20,000

17500

37500

4. 4) Consider a firm that has just built a plant, which cost $20,000. Each worker earns $5.00 per hour.

a)

Based on this information, fill in the table below.

Number of Worker Hours

Output

Marginal Product

Fixed

Cost

Variable

Cost

Total

Cost

Marginal

Cost

Average

Variable

Cost

Average

Total

Cost

0

0

20,000

50

8

20000

20,250

5

5

10

20000

20,500

5

5

8

20000

20,750

5

5

6

20000

21,000

5

5

4

20000

21,250

5

5

85

1900

2

20000

21,500

5

5

71.67

1950

1

20000

21,750

5

5

62.14

b)

In the example above, what price must the firm receive in order to keep producing in the short run?

The price the firm must receive in the short run is the price that covers the variable cost, so the firm must receive at least $5 per unit in the short run. In the long run, of course, the firm has to pay down the $20,000 facility.

c)

In the example above, assume that there is a maximum of 350 worker hours available (that is, there are no possibilities beyond the 350 worker hours shown in the table). What product price must the firm receive in order to remain in this industry in the long run?

In the long run, the firm needs to not only make a profit on each item but cover its fixed cost as well. This would be any price over and above the average total cost. So for example, at 350 workers, the firm needs to receive at least $62.14 to break even.

4) Consider a firm that has just built a plant, which cost $20,000. Each worker earns $5.00 per hour.

a)

Based on this information, fill in the table below.

Number of Worker Hours

Output

Marginal Product

Fixed

Cost

Variable

Cost

Total

Cost

Marginal

Cost

Average

Variable

Cost

Average

Total

Cost

0

0

20,000

50

8

20000

20,250

5

5

10

20000

20,500

5

5

8

20000

20,750

5

5

6

20000

21,000

5

5

4

20000

21,250

5

5

85

1900

2

20000

21,500

5

5

71.67

1950

1

20000

21,750

5

5

62.14

b)

In the example above, what price must the firm receive in order to keep producing in the short run?

The price the firm must receive in the short run is the price that covers the variable cost, so the firm must receive at least $5 per unit in the short run. In the long run, of course, the firm has to pay down the $20,000 facility.

c)

In the example above, assume that there is a maximum of 350 worker hours available (that is, there are no possibilities beyond the 350 worker hours shown in the table). What product price must the firm receive in order to remain in this industry in the long run?

In the long run, the firm needs to not only make a profit on each item but cover its fixed cost as well. This would be any price over and above the average total cost. So for example, at 350 workers, the firm needs to receive at least $62.14 to break even.

5)

A firm in an oligopolistic industry has the following demand, total cost, MR, and MC equations:

P = 600-20Q

TC = 700 + 160Q + 15Q2

MR = 600-40Q

MC = 160 + 30Q

Find:

a. quantity at which profit is maximized (Reminder: show your work).

This should be at the point where marginal revenue = marginal cost

600 -- 40Q = 160 + 30Q

440 = 70Q

Q = 6.28

b. maximum profit.

P at this level would be: 600 -- 20 (6.28) = $474.4

So profit would be Revenue -- Total cost

Revenue is 6.28(474.4) = 2979.23

Total cost at this level would be: 700 + (16)(6.28) + 15 (6.28) 2 = 1392.05

So maximum profit would e: $2,979.23 - $1,392.05 = $1,587.18

c. quantity at which revenue is maximized.

600 = 40Q

600 = 40Q

Q = 15

d. maximum revenue.

At Q = 15, P = $300

Revenue = $4,500

Note: I don't know if it's just me, but there is something wrong with this question. The equations don't make a lot of sense, such as marginal revenue declining the more you produce, so that past 15 units marginal revenue is negative. That makes no sense. You also have P, which goes below zero if you produce more than 30 units. So the answers you get don't really make a lot of sense. You can figure the math out, but I gave up trying to make sense of the actual numbers.

6)

Consider the fictitious industries depicted in the three industries shown below. For each industry, calculate the Herfindahl-Hirschman (HH) index and indicate whether or not the Department of Justice would consider it a concentrated industry.

a) Industry #1 Market Share of Each Firm:

Firm

Firm's Percent of Sales

Firm Alpha

60%

Firm Beta

10%

Firm Epsilon

10%

Firm Omega

10%

Firm Delta

10%

Herfindahl-Hirschman Index for Industry #1:

Would the Justice Department consider this a concentrated industry?

Using the Herfindahl-Hirschman Index formula:

.62 + 4 * .12 = 0.4

The U.S. threshold is 0.18, so yes this industry would be considered concentrated by the U.S. Department of Justice.

b) Industry #2 Market Share of Each Firm:

Firm

Firm's Percent of Sales

Verde Company

33%

Rouge Company

33%

Jaune Company

34%

Herfindahl-Hirschman Index for Industry #2:

Would the Justice Department consider this a concentrated industry?

.332 * 2 + .342 = .3334

Again, this industry would be considered to be concentrated.

c) Industry #3 Market Share of Each Firm:

Firm

Firm's Percent of Sales

Felucia

10%

Cato Neimoidia

10%

Mygeeto

40%

Saleucami

40%

Herfindahl-Hirschman Index for Industry #3:

Would the Justice Department consider this a concentrated industry?

.42 * 2 + .12 * 2 = 0.34

Yes, this would be considered concentrated

d) of the three industries shown, which would be considered the most concentrated?

The first industry, at 0.4, would be considered to be the most concentrated of the three, because the higher the number on the index the higher degree of concentration.

7) How is a monopolistically competitive industry like perfect competition? How is it like a monopoly?

A monopolistically competitive industry is similar to perfect competition in that sellers must compete aggressively with one another to win market share. Sellers must find ways to differentiate themselves in such a market environment. An example of perfect competition -- a row of date vendors at the Abu Dhabi Night Market. They must compete by differentiating themselves, such as with their charm or sales skills. Likewise, monopolistically competitive firms must seek creative ways to differentiate themselves from their competition.

In a monopolistically competitive industry, firms seek to use differentiation to create a monopoly for themselves. The idea is that if a firm becomes sufficiently differentiated, it can earn monopoly-like rents on its goods. Where a monopoly gains pricing power by not having competitors, monopolistic competitors gain pricing power by reducing the desire of consumers to use competitors.

8) Many markets show some characteristics of both -- competitive forces and evidence of market influence or power. In the company that you researched, did you see evidence of both? Describe the evidence of firm structure that you observed -- either evidence of competitive forces, or evidence that your firm had the ability to influence prices in the market, or evidence of both.

A good example of this can be found in Apple. Apple has a lot of market influence that derives from the company's strategy of creating differentiated products (different operating systems, for example) and engendering strong brand loyalty. This allows Apple to set its prices at a premium to the general market. Other computer-makers generally cannot do this, even ones with relatively strong brands like HP. However, Apple is still influenced by the market. The company can only charge a certain premium, after which it will begin to lose sales to cheaper substitutes. Customers may want an Apple computer but may see the price tag as being too high after a certain point. This effectively puts a ceiling on the price that Apple can charge.

9) Regarding market power

a. How can we detect market power?

Market power can be detected when firms are able to change their prices either at the supplier end or the buyer end without changing their demand. Thus, if firms can increase profit by changing prices.

b. Why should we care about detecting market power?

Detecting market power is important for investors to know which companies make the best investments. For firms, internally, it is valuable for them to understand their market power because this helps them to understand the degree to which they can influence their own profitability. Firms need to leverage their market power by changing prices, but they can only do so when they recognize that they have market power.

c. Please provide an example to support your statements. (Sources are not necessary on this test and personal observations are fine.)

A good example of this is with gas stations. Gas stations have tremendous market power. This is mitigated only somewhat by consumer knowledge and the time lag between price signals from the stations and consumer decisions (i.e. buying a car with better mileage). Gas stations know that if the price of crude is rising, they are in a better position to increase their prices. The cost of the gas they are selling may have been low -- purchased several months prior -- but this asymmetry of information provides them an opportunity to leverage their pricing power to increase their profits.

10) Describe at least two examples unique risks facing a multinational corporation that are not risks for a small local firm. For each risk, describe an action that a multinational firm might take to decrease its exposure to the risk.

A multinational faces a number of risks. Currency exchange rate risk is one -- MNCs do business in a number of currencies. When the value of those currencies changes, so too does the value of the costs and revenues of the MNC. There are a number of ways that MNCs decrease exposure. When possible, they do business in their home currency (for example an American firm insisting on selling in U.S. dollars). There are also hedging mechanisms such as forwards, futures and interest rate swaps that can lock in future prices, reducing the firm's exposure to foreign currency exchange risk.