Question

1. Cost curve estimation.  You and a group of 9 investors are interested in opening up a relatively large wholesale craft brewery operation to sell and ship specialty beers via the internet. Customers are primarily bars and restaurants. Part of your business plan involves assessing them most cost-efficient volume of beer to produce and distribute each year. To this end, you contacted several brewers associations, consulted with experts in the business, reviewed trade journals and collected estimates of total expenditures for a large set of breweries across the United States and Canada. These data are reported in column’s A and B of the “beer production costs” spreadsheet ( see below).   Q1: Use this data to estimate a cost curve and then Put your regression results in cell H2.

total expenditures per year ($1,000s, averaged over groups of breweries of same capacity)	capacity (1,000 bb1s) per year
195.22	1
810.27	2
591.78	3
1,342.35	4
1,915.61	5
2,003.14	6
1,727.58	7
2,863.54	8
884.61	9
3,508.42	10
1,216.58	11
4,170.70	12
3,831.40	13
3,963.27	14
5,409.94	15
4,871.02	16
5,532.12	17
4,654.85	18
4,008.82	19
4,571.65	20
4,459.94	21
5,948.31	22
4,774.38	23
2,159.74	24
3,690.03	25
5,756.83	26
3,980.78	27
4,218.47	28
4,816.53	29
8,391.56	30
8,542.18	31
4,627.00	32
9,564.62	33
6,231.67	34
2,902.75	35
5,392.48	36
2,991.46	37
1,144.31	38
1,660.64	39
7,650.07	40
2,752.20	41
13,112.65	42
13,652.02	43
5,102.94	44
10,290.01	45
12,307.84	46
6,235.05	47
7,582.25	48
6,344.05	49
5,909.06	50
13,162.89	51
8,955.16	52
15,875.48	53
7,617.45	54
4,553.70	55
3,568.83	56
20,227.45	57
14,570.19	58
5,826.64	59
6,750.42	60
8,385.15	61
9,710.43	62
13,921.87	63
25,251.10	64
16,335.71	65
11,041.33	66
24,352.56	67
10,122.02	68
10,518.31	69
23,886.06	70
19,895.86	71
17,598.34	72
28,384.11	73
30,223.77	74
22,292.95	75
19,171.24	76
25,677.27	77
21,597.64	78
38,039.96	79
38,107.86	80
27,894.94	81
31,374.81	82
35,944.08	83
24,587.37	84
25,887.29	85
28,862.45	86
39,225.46	87
41,124.94	88
33,463.49	89
33,827.72	90
31,207.26	91
42,523.71	92
51,865.68	93
59,537.79	94
41,635.65	95
58,594.86	96
44,490.04	97
54,895.81	98
68,593.77	99
72,877.54	100

Answer 1

Let us first plot the data as follows. We may observe that the output and cost have a non-linear relation. Hence, we may use higher order polynomial to estimate the cost function. Consider the following specification of the cost function to be estimated:

, where denotes capacity (1,000 bb1s) per year.

The regression results using excel can be presented below. The estimated resgression equation is:

As we may find, the linear, quadratic and cubic terms are statistically significant as their individual p-values are less than all conventional level of significance. Further, the terms are explaining more than 90% of variations in cost since the R-squared = 0.91. The overall regression is significant as evident by the p-value corresponding to the F-statistics. Hence, the above estimated cost function fits the data well.