7. Consider you own a small restaurant business. You collected data on the avera
ID: 1094795 • Letter: 7
Question
7. Consider you own a small restaurant business. You collected data on the average variable
costs of your business for the past 12 months. You have adjusted the cost data for
inflation by deflating with an appropriate price index. Your output (Q) and the associated
average variable cost (AVC) data are presented below:
(20 pts)
Obs
Q
AVC
1
22
$208
2
31
202
3
31
206
4
25
214
5
41
174
6
41
203
7
45
172
8
45
158
9
45
173
10
62
170
11
62
152
12
70
175
a. Use the data to run the appropriate regression to estimate the parameters for the empirical
cost function:
AVC a + bQ + cQ2
(Paste your computer printout here)
b. Using a 10 percent significance level, discuss suitability of the parameter estimates obtained
in part a. Consider both the algebraic signs and statistical significance of the parameter
estimates.
c. Present the estimated average variable cost, total variable cost, and short-run marginal cost
functions.
d. At what level of output does AVC reach its minimum value? What is the minimum value
of AVC at its minimum?
Obs
Q
AVC
1
22
$208
2
31
202
3
31
206
4
25
214
5
41
174
6
41
203
7
45
172
8
45
158
9
45
173
10
62
170
11
62
152
12
70
175
Explanation / Answer
Obs (X)
Q (Y)
X2
XY
Y2
1
22
1
22
484
2
31
4
62
961
3
31
9
93
961
4
25
16
100
625
5
41
25
205
1681
6
41
36
246
1681
7
45
49
315
2025
8
45
64
360
2025
9
45
81
405
2025
10
62
100
620
3844
11
62
121
682
3844
12
70
144
840
4900
Total = 78
520
650
Total = 3950
The linear regression equation is given by
Yc = bo + b1 x
b1 = 12X3950
Obs (X)
Q (Y)
X2
XY
Y2
1
22
1
22
484
2
31
4
62
961
3
31
9
93
961
4
25
16
100
625
5
41
25
205
1681
6
41
36
246
1681
7
45
49
315
2025
8
45
64
360
2025
9
45
81
405
2025
10
62
100
620
3844
11
62
121
682
3844
12
70
144
840
4900
Total = 78
520
650
Total = 3950
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