Question

The firm's demand is as follows:				Total variable costs are:
	Price	Quantity			Quantity	TVC
	$18	2			2	$15
	16	3			3	21
	15	4			4	27
	14	5			5	32
	13	6			6	37
	12	7			7	44
	10	8			8	52
				Fixed costs are $15
				at all quantities

QUESTION 1

What is the Marginal Revenue at a quantity of 5?

QUESTION 2

What is the Marginal Cost at a quantity of 7?  

QUESTION 3

Using the MR-MC rule, what is the profit maximizing quantity this firm should produce?

QUESTION 4

How much profit do they make at this quantity?

Answer 1

Question 1

It shall be noted that Total Revenue = TR = Price*Quantity

Hence,

Quantity	Price	TR
2	18	36
3	16	48
4	15	60
5	14	70
6	13	78
7	12	84
8	10	80

The Marginal Revenue (MR) is the rate of change in total revenue per unit change in the quantity.

MR = (TRq2 - TRq1)/(q2-q1)

Thus, the Marginal Revenue table is:

Quantity	Price	TR	MR
2	18	36	18
3	16	48	12
4	15	60	12
5	14	70	10
6	13	78	8
7	12	84	6
8	10	80	-4

Thus, at quantity 5, the marginal revenue MR is 10

Question 2

The Total Cost TC = TVC + TFC, that is sum of total-variable-cost and total-fixed-cost

Thus, the table is:

Quantity	TVC	TFC	TC
2	15	15	30
3	21	15	36
4	27	15	42
5	32	15	47
6	37	15	52
7	44	15	59
8	52	15	67

The marginal cost, MC is the rate of change of total cost per unit change in the quantity.

Hence, MC = (TCq2 - TCq1)/(q2-q1)

Hence, the table is:

Quantity	TVC	TFC	TC	MC
2	15	15	30	15
3	21	15	36	6
4	27	15	42	6
5	32	15	47	5
6	37	15	52	5
7	44	15	59	7
8	52	15	67	8

At quantity 7, the marginal cost is 7

Question 3

The profit-maximizing quantity is given by equilibrium condition MR = MC

If there is no quantity at which MR = MC, choose that quantity for which MR > MC but beyond which MC > MR

Quantity	MR	MC
2	18	15
3	12	6
4	12	6
5	10	5
6	8	5
7	6	7
8	-4	8

Thus, it can be observed that there is no quantity at which MR=MC

At Q = 6, MR > MC as 8>5

At Q=7, MR < MC as 6 < 7

Thus, the equilibrium quantity is 6

Question 4

At equilibrium quantity 7, the profit is given by:

Quantity	TR	TC
2	36	30
3	48	36
4	60	42
5	70	47
6	78	52
7	84	59
8	80	67

Profit = TR - TC

Profit = 78-52

Profit = 26