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, and MC 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

Q	P	PROFIT	MR	T VC	TC	MC	ATC	AVC	TFC
1	6	0	6	4	6	4	6	4	2
2	12	4	6	6	8	2	4	3	2
3	18	7.98	6	8	10	2	3.33	2.66	2
4	24	7	6	11	13	3	3.25	2.75	2
5	30	13	6	15	17	4	3.4	3	2
6	36	13.98	6	20	22	5	3.66	3.33	2
7	42	16.03	6	26	28	6	3.71	3.71	2
8	48	13	6	33	35	7	4.375	4.125	2
9	54	13.05	6	41	43	8	4.55	4.55	2
10	60	10	6	50	52	9	5	5	2

In order to complete the table first, the fixed cost is to be found.

Now according to the table, the MC of manufacturing 0 units is 2 hence the initial fixed cost is to be 2 units.

The fixed cost stays constant throughout.

The TC is found by adding FC+MC=AC

ATC=AC/Q.

TFC=FC*Q.

AVC=ATC/Q.

MC=TC(n)-TC(n-1).

USe the above formula to fill the table.

C) In order to maximize profit use the condition MC=MR which is given at a point where both are 6 units that are at quantity 7 units.

D)The total profit would be at 7units and would correspond to the profit of 16.03 units.

The point is graphically represented by the point where the line MC cuts the constant line MR.