Question

Assume you run a bakery that produces organic bread which is characterized as being a very competitive industry with a large number of bakeries. You know that you, as a single bakery, cannot impact bread prices observed in the marketplace. Assume you are attempting to maximize profit. You have hired an economist to provide a forecast of next month's market price for organic whole wheat bread. He returns an analysis that indicates that the most likely price next month will be $4:00 per loaf. The question you have is how many thousands of whole wheat loaves you should produce next month assuming this price forecast is accurate.

Using data over the last 5 years, the economist has estimated a statistical model showing the relationship between your costs of production and the number of thousands of whole wheat loaves manufactured. This statistical relationship is given below (again, quantity is measured in terms of 1000 of loaves, that is 7.5 = 7500 loaves and all costs are in $000, that is 2.5 = $2500).

?? = 5 + 10? − 0.9?^2 + 0.04?^3

?? = 10 − 1.8? + 0.12?^2

where TC are in $000, Q is measured in 1000 loaf units, and MC represents marginal costs.

a) What is the equation for the total fixed costs (TFC) of production? What is the equation for the average fixed costs (AFC) of production?

b) What is the equation for the total variable costs (TVC) of production? What is the equation for the average variable costs (AVC) of production? What is the equation for the average total costs (ATC) of production?

c) Using Excel, graph the MC, AVC and AFC for production from 1000 to 20000 loaves using 500 loaf production increments on the same graph. (Hint: Don't overlook the fact that production is measured in 1000 loaf units.)

d) How many loaves of organic whole wheat bread should be produced such that AVC is minimized? (Hint: What characterizes this level of output in terms of the cost curves?)

e) What is the profit maximizing level of output given the anticipated $4.00 per loaf market price? What is the level of profit using the most reasonable profit maximizing output level? Would the firm want to produce given these prices? (Hint: What characterizes the profit maximizing output with respect to the above cost curves?)

Answer 1

(a)

From TC function,

TFC = 5 (since TFC is independent of Q)

AFC = TFC/Q = 5/Q

(b)

TVC = 10Q − 0.9Q² + 0.04Q³

AVC = TVC/Q = 10 - 0.9Q + 0.04Q²

ATC = AFC + AVC = (5/Q) + 10 - 0.9Q + 0.04Q²

(c)

Data table used:

Q ('000)	MC ($'000)	AVC ($'000)	AFC ($'000)
1	8.32	9.14	5
1.5	7.57	8.74	3.33
2	6.88	8.36	2.5
2.5	6.25	8	2
3	5.68	7.66	1.67
3.5	5.17	7.34	1.43
4	4.72	7.04	1.25
4.5	4.33	6.76	1.11
5	4	6.5	1
5.5	3.73	6.26	0.91
6	3.52	6.04	0.83
6.5	3.37	5.84	0.77
7	3.28	5.66	0.71
7.5	3.25	5.5	0.67
8	3.28	5.36	0.625
8.5	3.37	5.24	0.59
9	3.52	5.14	0.56
9.5	3.73	5.06	0.53
10	4	5	0.5
10.5	4.33	4.96	0.48
11	4.72	4.94	0.45
11.5	5.17	4.94	0.43
12	5.68	4.96	0.42
12.5	6.25	5	0.4
13	6.88	5.06	0.38
13.5	7.57	5.14	0.37
14	8.32	5.24	0.36
14.5	9.13	5.36	0.34
15	10	5.5	0.33
15.5	10.93	5.66	0.32
16	11.92	5.84	0.3125
16.5	12.97	6.04	0.30
17	14.08	6.26	0.29
17.5	15.25	6.5	0.29
18	16.48	6.76	0.28
18.5	17.77	7.04	0.27
19	19.12	7.34	0.26
19.5	20.53	7.66	0.26
20	22	8	0.25

Graph:

(d)

AVC is minimized when MC = AVC (since MC intersects AVC at its minimum point).

10 - 1.8Q + 0.12Q² = 10 - 0.9Q + 0.04Q²

0.08Q² = 0.9Q

0.08Q = 0.9 (Assuming Q is non-zero)

Q = 11.25 (thousands)

NOTE: As per Answering Policy, 1st 4 parts are answered.