Question

Consider the following hourly demand and cost schedule for a firm facing a fixed price of $ 6.00 per unit. (Tπ, is Total Profit).

Q    P             TR   MR    TFC       TVC          TC         MC           ATC          AVC         Tπ

                                                                                                                                                             

0    $6.00                                                         $2.00            

1                                                         4             

2                                                        6             

3                                                        8             

4                                                       11             

5 15                     

6                                                       20

7 26             

8                                                      33          

  9                                                      41          

10                                                     50

11                                                     60

                                                                                                                                      

1. Complete the columns for ATC, AVC, andMC as well as those for (TC),TVC, & TFC.

2. Draw the curves for Demand, MR (Marginal Revenue), ATC, AVC, and MC, all in one diagram. Also draw the Total Revenue (TR), Total Cost (TC), TVC, and TFC in a second diagram right below the first one.

3. Determine, in order to maximize profit, how many units should this firm produce and why?

4. Calculate the total profit at the profit-maximizing level and demonstrate it graphically and geometrically in the diagrams wherever applicable.

Answer 1

Solution:

a) Given, price is fixed.

Q	P	TR	MR	TFC	TVC	TC	MC	ATC	AVC	Tπ
0	$6	0	--	2	0	$2	--	--	--	-2
1	$6	6	6	2	4	6	4	6	4	0
2	$6	12	6	2	6	8	2	4	3	4
3	$6	18	6	2	8	10	2	3.33	2.67	8
4	$6	24	6	2	11	13	3	3.25	2.75	11
5	$6	30	6	2	15	17	4	3.4	3	13
6	$6	36	6	2	20	22	5	3.67	3.33	14
7	$6	42	6	2	26	28	6	4	3.71	14
8	$6	48	6	2	33	35	7	4.38	4.13	13
9	$6	54	6	2	41	43	8	4.78	4.56	11
10	$6	60	6	2	50	52	9	5.2	5	8
11	$6	66	6	2	60	62	10	5.63	5.45	4

Formula used:

Total Cost (TC) = (AVC + AFC) X Output

Total Variable Cost (TVC) = AVC X Output

Total Fixed Cost (TFC) = TC – TVC

Marginal Cost (MC) = Change in Total Costs / Change in Output

Marginal Revenue (MR) = Change in Total Revenue / Change in output

Total Revenue (TR) = Price X Quantity

Economic Profit = TR – TC > 0

Average Total Cost (ATC) = Total Cost / Output

Average Variable Cost (AVC) = Total Variable Cost / Output

b) The following graphs illustrate TR, MR, TC, TVC, TFC, ATC, AVC, MR=MC, P and Demand.

a) There are two ways to determine the maxium profit. First, the profit is maximised when the difference between the total revenue (TR) and total cost (TC), that is, the total profit (Tπ) is the largest. In this case, the largest difference is $14 and it occurs twice for two different quantities, once for 6 units and again for 7 units of the good. So either 6 units should be produced or 7 units.

Second, the profit is maximised at the quantity corresponding to which the marginal cost (MC) is equal to the marginal revenue (MR). In this case, corresponding to the quantity 7 units, the MR=MC=$6. So, the firm should produce 7 units to maximise its profit because at this quantity MR=MC, the firm’s marginal profit is zero when its total profit is maximum and constant. When this happens, it is not possible for the firm to make any extra profit by producing and selling any extra unit of output. So, the firm maximises it total profit when producing and selling the extra unit adds as much as to revenue as to the cost.

b) The total profit at the profit-maximizing level is $14. It is shown in the above graph as MR=MC and also as the maximum difference between TR and TC.