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.

Average Average Total Total Marginal Marginal Total Variablel Profit Cost Output Cost Revenue Cost Revenue Cost 0 3 XxX XXX 1 7 10 2 20 3 10 30 4 12 40 16 50 6 22 60 7 30 70 8 40 80 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

Answer

When output(Q) is '0' , firm's total cost(TC) = 3 .

$\therefore$ The firm's fixed cost (FC) = 3

Now, Total cost = Fixed cost + Variable cost(VC)

Or, VC = TC - FC

$\therefore$ The firm's VC = TC - 3 , for each level of output, and associated TC.

Average total cost(ATC) = TC / Q

Average variable cost (AVC) = VC / Q

Marginal Cost (MC) is the change in TC due to change in one additional level of output(Q).

$\therefore$ MC = d(TC) / dQ

Marginal revenue(MR) is the change in total revenue(TR) due to change in one additional unit of output.

$\therefore$ MR = d(TR) / dQ

Profit = TR - TC

Now, calculating all the values, and putting them in the table;

Output(Q)	Total Cost(TC)	Total Revenue(TR)	Profit	Marginal Cost(MC)	Marginal Revenue(MR)	Average Total Cost(ATC)	Variable Cost(VC)	Average Variable Cost(AVC)
0	3	0	-3	xxx	xxx	-	-	-
1	7	10	3	4	10	7	4	4
2	9	20	11	2	10	4.5	6	3
3	10	30	20	1	10	3.3	7	2.3
4	12	40	28	2	10	3	9	2.25
5	16	50	34	4	10	3.2	13	2.6
6	22	60	38	6	10	3.7	19	3.17
7	30	70	40	8	10	4.3	27	3.86
8	40	80	40	10	10	5	37	4.63
9	52	90	38	12	10	5.8	49	5.44
10	68	100	32	16	10	6.8	65	6.5

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Based on the information in the table​ above, the marginal cost​ (MC), and marginal revenue(MR) curves at each rate of output are shown in the figure below;

OD 6 has 9 5 0 3 2 1 -MR -MC OT -

In the above figure, we are measuring output on the horizontal axis, and 'MR', and 'MC' on the vertical axis. The green curve is the 'MC' curve, and the purple line shows the 'MR'.

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Based on the information in the table​ above, the average total costs ​ (ATC) and average variable costs(AVC) at each rate of output are shown in the figure below;

6.5 5.44 - ATC 3.86 AVC 0 ? € 6787 ha of

In the above figure, we are measuring output on the horizontal axis, and 'ATC', and 'AVC' on the vertical axis. The blue curve is the ATC curve, and the red curve is the AVC curve.

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The short-run supply curve for this perfectly competitive firm is shown in the following figure;

- ATC --AVC --MC + 2 0 s 9 t of things

In the short-run, a perfectly competitive firm supplies the output, for which the marginal cost(MC) is equal to or above the minimum point of average variable cost(AVC). So the upward portion of the MC curve, which is above the AVC curve, is the short-run supply curve of a perfectly competitive firm. In the above figure, the yellow portion of the MC curve, is the firm's supply curve. So here, the firm's supply curve is 'PN' part of MC curve. Point 'P' is the minimum point of AVC curve.

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Based on the marginal analysis, the perfectly competitive firm produces the profit-maximizing level of output, where MR = MC.From the table, we see that at 8 units of output, the firm's MC = MR = 10.

So the firm's profit- maximizing rate of output is 8 units.

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