Question

The table below represents the output and cost structure for a firm. The market is perfectly​ competitive, and the market price is ​$10. Total costs include all implicit opportunity costs.

Output	Total Cost	Total Revenue	Profit	Marginal Cost	Marginal Revenue	Average Total Cost	Average Variablel Cost
0	3	0		xxx	xxx
1	7	10
2	9	20
3	10	30
4	12	40
5	16	50
6	22	60
7	30	70
8	40	80
9	52	90
10	68	100

1. Calculate the firm’s profit at each rate of output and fill in the values in the table.
2. Calculate firm's marginal cost and marginal revenue at each rate of output and fill in the values in the table.
3. Calculate the firm’s average total costs and average variable costs at each rate of output and fill in the values in the table.
4. Based on the information in the table​ above, plot marginal cost​ (MC) at each rate of output. Properly label this line.
5. ​Based on the information in the table​ above, plot marginal revenue​ (MR) at each rate of output. Properly label each line.
6. Based on the information in the table​ above, plot average total costs ​ (ATC) and average variable costs at each rate of output. Properly label each line.
7. Highlight in yellow the short-run supply curve for this perfectly competitive firm.
8. Based on marginal​ analysis, what is the​ profit-maximizing rate of output for the firm?

Answer 1

Below is the completed table:

Output	TR	TC	Profit	MR	MC	TFC	TVC	AFC	AVC	AC
0.00	0.00	3.00	-3.00			3.00	0.00
1.00	10.00	7.00	3.00	10.00	4.00	3.00	4.00	3.00	4.00	7.00
2.00	20.00	9.00	11.00	10.00	2.00	3.00	6.00	1.50	3.00	4.50
3.00	30.00	10.00	20.00	10.00	1.00	3.00	7.00	1.00	2.33	3.33
4.00	40.00	12.00	28.00	10.00	2.00	3.00	9.00	0.75	2.25	3.00
5.00	50.00	16.00	34.00	10.00	4.00	3.00	13.00	0.60	2.60	3.20
6.00	60.00	22.00	38.00	10.00	6.00	3.00	19.00	0.50	3.17	3.67
7.00	70.00	30.00	40.00	10.00	8.00	3.00	27.00	0.43	3.86	4.29
8.00	80.00	40.00	40.00	10.00	10.00	3.00	37.00	0.38	4.63	5.00
9.00	90.00	52.00	38.00	10.00	12.00	3.00	49.00	0.33	5.44	5.78
10.00	100.00	68.00	32.00	10.00	16.00	3.00	65.00	0.30	6.50	6.80

• TC = TFC+TVC,
• TFC remains the same for all units of output.
• TVC is 0 at o output
• So TC at 0 unit = TFC = 3
• Using this we can calculate the TVC at all units
• AFC = TFC/output
• AVC = TVC/output
• AC = TC/output
• 
  • So for 2 units of output:
  • 
  • 
  • Similarly, for all units or output the MC is calculated
• 
  • MR is calculated using the difference of TR instead of TC as in case of MC
• Profit = TR-TC

Below are the 3 required graphs

Short run supply curve is the upward sloping part of the MC curve so only the part from the 4rth unit onwards

Profit is maximized where MR = MC and therefore where the MC curve intersects the MR curve. So that happens at the output of 10 units. The profit is the same for 7 units also but the total revenue is higher at 8th unit