Question

Q	P	Tr	Mr	TFC	TVC	TC	MC	ATC	AVC	T(π)
0	$19.00					$4.00
1	$18.00						4
2	$17.00						2
3	$16.00						1
4	$15.00						2
5	$14.00						3
6	$13.00						4
7	$12.00						5
8	$11.00						6
9	$10.00						7

                 

Complete the columns for TR, MR, TFC, TVC, TC, ATC, AVC, and MC, as well as those for (TC), TVC, & TFC. Draw the curves for Demand (Price Vs. Quantity), MR (Marginal Revenue), ATC, AVC, and MC, all in one diagram. Also draw the Total Revenue (TR), Total Cost (TC), TVC, andTFC in a second diagram right below the first one.

1. Determine, in order to maximize profit. How many units this firm should produce and explain.

2. Demonstrate the geometric areas (rectangles) of Total Revenue, Total Cost and Total Profit at the profit-maximizing level and calculate the values of each in the diagram above (and not the one below).

3. Show the Total Revenue, Total Cost and Total Profit at the profit-maximizing level in the diagram below.

                           

Answer 1

Q	P	TR	MR	TFC	TVC	TC	MC	ATC	AVC	T(π)
0	19	0	-	4	0	4	-	-	-	-4
1	18	18	18	4	4	8	4	8	4	10
2	17	34	16	4	6	10	2	5	3	24
3	16	48	14	4	7	11	1	3.666667	2.333333	37
4	15	60	12	4	9	13	2	3.25	2.25	47
5	14	70	10	4	12	16	3	3.2	2.4	54
6	13	78	8	4	16	20	4	3.333333	2.666667	58
7	12	84	6	4	21	25	5	3.571429	3	59
8	11	88	4	4	27	31	6	3.875	3.375	57
9	10	90	2	4	34	38	7	4.222222	3.777778	52

Total revenue is calculated as;

TR = P*Q

Marginal revenue is the additional revenue generated when one more unit of output is sold.

Total cost is the;

TC = TFC + TVC

Marginal cost is the additional cost incurred when one more unit of output is produced.

Average total cost is;

ATC = TC/Q

Average variable cost is;

AVC = TVC/Q

Profit is calculated as;

T(π) = TR - TC

The blue line is the demand curve which shows the relationship between price and quantity demanded. The red line and grey line is the marginal revenue and the marginal cost curve. The yellow line and light blue line is the average total cost and the average variable cost curve.

The blue curve is the total revenue curve, yellow curve is the total cost. Grey and red curves are total variable cost and total fixed cost.

a)

In order to maximise profit, firm should produce where marginal revenue is equal to marginal cost.

As we can see from the table and figure above, firm's profit is maximized at output level, Q = 7.

b.

From the above figure, the total revenue at profit maximising level, Q = 7 is the area of rectangle ABCD.

TR = Ar ABCD
= 7*12
TR = 84

The total cost at profit maximising level, Q = 7 is the area of rectangle CDEF.

TC = Ar CDEF
= 7*3.571429
TC = 25

The total profit at profit maximising level, Q = 7 is the area of rectangle ABEF, which is the difference between ar ABCD and ar CDEF,

Proft = Ar ABCD - Ar CDEF
= 84 - 25
Profit = 59

c)

At profit maximising level, Q = 7 total revenue is, TR = 84

Total cost , TC = 25

Profit = TR-TC
Profit = 59