SUDOKU IN ECONOMICS
Try filling in this table.
Q
0
FC
VC
TC
MC
-------
AFC
-------
20
5
AVC
------10
8
13
96
10
12
108
The formulas you need are
FC + VC = TC
MC = Change in total cost/Change in quantity = Change in variable cost/Change in quantity
AFC = FC/Q
AVC = VC/Q
ATC = TC/Q = AFC + AVC
Answers on the next page.
ATC
-------
8
9
Here’s the completed table
Q
0
2
5
FC
40
40
40
40
40
40
10
12
VC
0
20
25
56
80
108
TC
40
60
65
96
120
148
MC
------10
1.67
AFC
------20
8
AVC
------10
5
ATC
------30
13
12
14
4
3.33
8
9
10
12.33
These are the steps I took; obviously you could have done a different order.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
VC = 0 when Q = 0
FC at Q=5 is 40 using AFC = FC/Q
When you know one FC, you know them all. FC is 40 in all rows.
TC at Q=0 is $40 using FC + VC = TC
TC at Q=? (second row) is 60 using FC + VC = TC
VC at Q=? (fourth row) is 56 using FC + VC = TC
Q = 2 (second row) using AVC = VC/Q
TC at Q=? (last row) using FC + VC = TC
When Q=2, AFC = 20 using AFC = FC/Q and ATC = 30 using ATC = TC/Q
MC = 10 at Q=2, using formula for MC
AVC at Q=5 is 5, using AFC + AVC = ATC
VC=25 at Q = 5 using AVC = VC/Q, and TC = 65 at Q=5 using ATC = TC/Q
MC=1.67 (or 5/3) at Q=5
VC=80 at Q=10 using AVC = VC/Q
TC=120 at Q=10 using FC + VC = TC
AFC=4 at Q=10 using AFC = FC/Q and ATC = 12 at Q=10 using ATC = TC/Q
Q=12 in the last row using AVC = VC/Q
AFC=40/12=3.33 at Q=12 using AFC = FC/Q, and ATC=148/12=12.33 at Q=12 using ATC = TC/Q
MC=14 at Q=12 using formula for MC
How are you doing so far? Now we come to that row highlighted in yellow. We seem to have a
problem. You need the quantity to get any of the averages or the marginal, however you’d need one of
those to get the quantity you’re missing. Here’s a hint. Look at the rows in blue.
Q
0
2
5
10
12
FC
40
40
40
40
40
40
VC
0
20
25
56
80
108
TC
40
60
65
96
120
148
MC
------10
1.67
AFC
------20
8
AVC
------10
5
ATC
------30
13
12
14
4
3.33
8
9
10
12.33
Give up? With these cells, we can expand the formula for marginal cost to find the missing quantity.
Here’s how this works.
𝑀𝐶 =
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 𝑇𝐶(𝑎) − 𝑇𝐶(𝑏)
=
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦
𝑄(𝑎) − 𝑄(𝑏)
We agree that this is MC. We simply subtract two different TC’s, two different Q’s and divide the
differences. What if we plugged in the numbers in the blue cells to their proper location? We’d get
12 =
120 − 96
10 − 𝑄
It’s not the prettiest algebra, but from this you can get the missing quantity.
12 =
24
,
10 − 𝑄
10 − 𝑄 =
24
, 10 − 𝑄 = 2 , 𝑄 = 8
12
Now that we know that missing quantity, the rest of the missing cells in that row are cake.
Q
0
2
5
8
10
12
FC
40
40
40
40
40
40
VC
0
20
25
56
80
108
TC
40
60
65
96
120
148
MC
------10
1.67
10.33
12
14
AFC
------20
8
5
4
3.33
AVC
------10
5
7
8
9
ATC
------30
13
12
10
12.33
FC
VC
TC
MC
AFC
AVC
ATC
-----
-----
-----
-----
Done.
Try this one.
Q
0
4
5
30
15
3
65
60
10
3
5
Answer Key is on the next page. Try filling it in on your own before you look.
5
Q
FC
VC
TC
MC
AFC
AVC
ATC
0
20
0
20
-----
-----
-----
-----
4
20
20
40
5
5
5
10
10
20
30
50
1.67
2
3
5
15
20
45
65
3
1.3
3
4.3
18
20
60
80
5
1.11
3.33
4.44
If you did this without any trouble, there’s nothing I can throw at you on the exam that should give you
trouble.