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# Mathematics problem

1. Complete the following problems:

a. Using Figure 9.2 (p. 207), suppose P0 is \$10 and P1 \$11. Suppose a new firm with the same LRAC
curve as the incumbent tries to break into the market by selling 4,000 units of output. (Taylor & Greenlaw,

2014, p. 223).

i. Estimate from the graph what the new firm�s average cost of producing output would be.
ii. If the incumbent continues to produce 6,000 units, how much output would be supplied to the market by

the two firms?

iii. Estimate what would happen to the market price as a result of the supply of both the incumbent firm

and the new entrant.

1. Approximately how much profit would each firm earn?

b. Using Figure 9.6 (p. 217) draw the demand curve, marginal revenue and marginal cost curves. (Taylor

& Greenlaw, 2014, p. 223).

i. Identify the quantity of output the monopoly wishes to supply and the price it will charge.
ii. Suppose demand for the monopoly�s product increases dramatically. Draw the new demand curve.

1. What happens to the marginal revenue as a result of the increase in demand?
2. What happens to the marginal cost curve?
3. Identify the new profit-maximizing quantity and price.
c. Use the following table for this problem: (Taylor & Greenlaw, 2014, p. 242).

Price Quantity TC
\$25.00 0 \$130

MATH PROBLEM 2

\$24.00 10 \$275
\$23.00 20 \$435
\$22.50 30 \$610
\$22.00 40 \$800
\$21.60 50 \$1,005
\$21.20 60 \$1,225

Andrea�s Day Spa began to offer a relaxing aromatherapy treatment. The firm asks you how much to
charge to maximize profits. The demand curve for the treatments is given by the first two columns. The
total costs are given in the third column. For each level of output, calculate total revenue, marginal

revenue, average cost, and marginal cost.

i. What is the profit-maximizing level of output for the treatments and how much will the firm earn in

profits?

Complete the following problems:

a. A \$10,000 ten-year bond was issued at an interest rate of 6%. It is now year 9 and you are thinking
about buying the bond from its owner. Interest rates are now 9%. (Taylor & Greenlaw, 2014, p. 403).
i. Would you now expect to pay more or less than \$10,000 for the bond? Why?
ii. Calculate what you would be willing to pay for the bond.

b. Consider the following stock ownership situation (Taylor & Greenlaw, 2014, p. 403).

Investor 1: 20,000 shares
Investor 2: 18,000 shares
Investor 3: 15,000 shares
Investor 4: 10,000 shares

MATH PROBLEM 3

Investor 5: 7,000 shares
Investors 6 � 11: 5,000 shares each

ii. What is the minimum number of investors it would take to vote to change the top management of the

company?

iii. Which investors would this involve?

iv. In 1-2 paragraphs discuss if any one investor would be able to make corporate changes without the

agreement of the other investors.

Math Problem
Name
Institution

MATH PROBLEM 4

Math Problem
a) Marginal Gain in Output

Marginal gain = change in total output/change in quantity
4-5 – ([80 * 5] – [72 *4])/ (80 – 72) = 15 units per unit of labor
5-6 – ([84 *6] – [80 * 5])/ (84 – 80) = 26 units per unit of labor
The above marginal output follows the principles of diminishing marginal returns.
b) Average Total, Variable and Marginal Costs

c)
Quantity Unit
Price
Fixed
Cost
Total
Variable
costs

Total
Revenue

Marginal
Revenue

Total Cost
(Fixed +
variable)

Marginal
Cost
1 \$20 \$20 \$20 \$20 – 20 + 20 = \$40 –
2 \$20 \$20 \$25 \$40 20 20 + 25 = \$45 \$5
3 \$20 \$20 \$35 \$60 20 20 + 35 = \$55 \$10
4 \$20 \$20 \$50 \$80 20 20 + 50 = \$70 \$15
5 \$20 \$20 \$80 \$100 20 20 + 80 = \$100 \$30

MATH PROBLEM 5

The profit maximizing output is when; marginal cost = marginal revenue. Since there is no
equilibrium in MC and MR, the closest maximizing quantity is 4.
d) Output and Costs
Quantity Fixed
Cost
Total
Variable
costs

Average
Variable
Cost

Total
Cost
(Fixed +
variable)

Marginal Cost

1 \$250 \$450 450 \$700 \$700
2 \$250 \$700 350 \$950 \$250
3 \$250 \$1000 333.33 \$1250 \$300
4 \$250 \$1350 337.5 \$1600 \$350
5 \$250 \$1750 350 \$2000 \$400
6 \$250 \$2200 366.67 \$2450 \$450
7 \$250 \$2700 385.71 \$2950 \$500

ii)

The zero profit point is at the minimal point of the average curve at point c while the
shutdown point is where price equals the average variable cost.

MATH PROBLEM 6
If the firm sells the computers at \$300, it will be making a loss when compared to prices
at \$500. This is because profits at \$300 will earn profits at 03cb while profits made at \$500 will
be 03da.

1. Complete the Following Problems

Figure 9.2

Selling 4,000 units of output will attract a price above p 1 .
II) The total amount of production supplied by the two firms would be 10,000 units.
III) The market price will be lowered since there would be more supply of goods from both firms.
b)

MATH PROBLEM 7

I) The monopoly firm wishes to supply its commodities at 4 units and at a price of 900.
II) If the demand increases, the demand curve will shift outwards.
Therefore, the marginal revenue will increase while the marginal cost curve shifts inwards. The
new profit maximizing quantity and price will be where the new marginal cost curve intersects
with the marginal revenue curve.
Price Quantity TR TC AC MR MC
\$25.00 0 0 \$130 \$0 – –
\$24.00 10 \$240 \$275 \$27.5 24 14.5
\$23.00 20 \$460 \$435 \$21.75 22 16.0
\$22.50 30 \$675 \$610 \$20.33 21.5 17.5
\$22.00 40 \$880 \$800 \$20 20.5 19.0
\$21.60 50 \$1080 \$1,005 \$20.1 20.0 20.5
\$21.20 60 \$1272 \$1,225 \$20.4 19.2 22.0
The profit maximizing level is where MC equals MR which is either arrived at by
producing 40 or 50 units. Therefore, the profit at 40 units will be \$80 and the profit
produced at 50 units will be \$75. For that reason, the firm’s maximizing profit level will
be 40 units.

1. Complete the Following Problems

MATH PROBLEM 8
I) one would expect not to pay more for the bond since an increase in interest rates
indicates an increase in the value and risk of bonds.
II) Future value = principle amount * (1 + rate) time ; 10,000 * (1 + 0.09) 9 = 21, 718
Bonds i – 4.5%, n – 20 semiannual periods, interest (PMT) – 300 semiannual (6% * 10, 000 *
6/12),
Therefore, present value of the bond – 300 * [1/(1 + 0.045) 20 ]
b) The minimum number of investors required to change the top management of a company is 3.
III) The investors would be 1, 2, and 3 who make 53% in ownership and can gather votes.
IV) Making corporate changes requires one to have more shares than the rest. This means
that a shareholder who has the most number of shares can gather more votes (Taylor &
Greenlaw, 2014). Therefore, one investor can make corporate changes. In this case, investor
number 1 can make organizational changes without agreeing with other investors. This is
because he has 20,000 shares which are 20% higher than all the rest. After all, having more
shares means that one is capable of gaining more votes and has the highest ownership
percentage.

MATH PROBLEM 9

References

Taylor, T., & Greenlaw, S. A. (2014). Principles of microeconomics.