Question

Suppose that Jessica faces the following total cost function: C(y) = 2y2 + y + 200 Note that 200 denotes the fixed cost component. Use this information in answering this part of the submission question. (a) Find the Marginal cost function, Average Cost function, Average Variable cost function and the Average fixed cost function. Once you obtain these, sketch them on the grid below.

Answer 1

a) MC = 4y + 1

AC = 2y + 1 + 200/y

AVC = 2y + 1

AFC = 200/y

Using the following table to draw the graphs

y	MC	AC	AVC	AFC
1	5	203	3	200
2	9	105	5	100
3	13	74	7	67
4	17	59	9	50
5	21	51	11	40
6	25	46	13	33
7	29	44	15	29
8	33	42	17	25
9	37	41	19	22
10	41	41	21	20
11	45	41	23	18
12	49	42	25	17
13	53	42	27	15
14	57	43	29	14
15	61	44	31	13
16	65	46	33	13

Cost 1 2 3 4 5 6 7 10 11 12 13 14 15 16 8 9 Output (y) - - MC ....... AC — AVC --- AFC

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b) The short run supply curve corresponds to the marginal cost curve that lies above the average variable cost curve. In the above figure, the MC lies above the AVC at all the points, so MC is the short-run supply curve.

Given p= 61, the output supplied equals

MC = p

4y + 1 = 61

y = 15

Jessica's producer surplus = Total revenue - total variable cost

PS = 61 * 15 - 2*(15)² + 15

= 915 - 465

Jessica's producer surplus = 450

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c) Long-run supply curve- the marginal cost curve above the minimum point of average cost curve represents the long-run supply curve of the firm.

In the question, the MC curve above 10 units of output represents long-run supply curve.

Given p =61,

the output supplied equals

AC = MC

2y + 1 + 200/y = 4y + 1

200/y = 2y

y² = 100

y = 10

Jessica's Profit = Total Revenue - Total Cost

= 61* 10 - 2 * 100 + 10 + 200

= 610 - 410

Jessica's Profit = 200

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d) Yes, Jessica strictly supplies a positive amount in both short run and long run because the price charged lies above the minimum cost curve for long-run and above minimum average cost curve for short run.

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