1. A firm is expected to earn $10,000, $25,000, $48,000, and $75,000 during the next four years, after which it will be dissolved. What is the present value of the firm if the discount rate is 8%?

You need to find the present value for cash flow for each year in the next four years by using the present value formula as follows:-

PV = FVn where PV is the present value
(1 + i)n FV is the future value in that particular year
i is the discount rate
n is the period.

Year 0 1 2 3 4
10,000 25,000 48,000 75,000

PV = 10,000 + 25,000 + 48,000 + 75,000
(1 + 0.08)1 (1 + 0.08)2 (1 + 0.08)3 (1 + 0.08)4

PV = 10,000(0.9259) + 25,000(0.8573) + 48,000(0.7938) + 75,000(0.7350)
PV = 123,918.90

2. Jane has compiled the following list of expenses after completing one year of college. Assume that Jane would be living with her parents and working if she weren't attending college. Use this information to calculate Jane's economic cost of attending college for one year.

Tuition $ 8,000
Dormitory room 4,000
Books and supplies 1,000
Food plan 3,000
Foregone income 19,000
Entertainment expenses 1,000
Clothing 2,000
Health insurance 1,000

Opportunity cost is a term used in economics, to mean the cost of something in terms of an opportunity foregone (and the benefits that could be received from that opportunity), or the most valuable foregone alternative.

Therefore, if Jane decides to attend college for one year. Her economic cost is the forgone income of $19,000 because she will lose the opportunity to earn income.

3. A firm's demand function is defined as Q = 30 - P. Use this function to calculate total revenue when price is equal to 5 and when price is equal to 6. What is marginal revenue equal to between P=5 and P=6. (Hint: total revenue = P x Q and marginal revenue = change in total revenue / change in quantity)

First you need to find the Q when price is equal to 5 and 6 by replacing into the firm's demand function as follows: -

Q = 30 - P
Q = 30 - 5 = 25
Q = 30 - 6 = 24

Then, we need to find the total revenue when price is equal to 5 and 6 by replacing into the total revenue function as follows: -

Total revenue = P x Q

Total revenue = 5 x 25 = 125
Total revenue = 6 x 24 = 144

Then, we can calculate the marginal revenue by using the marginal revenue function as follows: -

Marginal revenue = change in total revenue / change in quantity
= (144 - 125)/(25 - 24)
= 19/1
= 19

4. Use the demand schedule that is presented in the table below to determine the optimal rate of production and price when the firm has the following marginal cost function: MC = 1 + Q. (Hint: the firm should produce the product as long as MR is greater than or equal to MC)

Quantity 1 2 3 4 5 6 7 8 9 10
Price 80 60 48 40 34 29 25 20 15 10

ANY IDEA How to solve those problems?

MC = Marginal Cost
MR = Marginal Revenue
Q = Quantity

Quantity MR Total Revenue MC Total Profit/Loss
(1) (2) (3) = (1) x (2) (4) (5) = (3) - (4)

1 80 80 2 78
2 60 120 3 117
3 48 144 4 140
4 40 160 5 155
5 34 170 6 164
6 29 174 7 167
7 25 175 8 167
8 20 160 9 151
9 15 135 10 125
10 10 100 11 89

The firm should produce the product until 9 units because the tenth unit of the product will cause the profit to decrease due to lower MR than MC.