This is a great little exercise, one that's helped greatly if you can
use a spreadsheet. Let's start with the definitions:
TFC: total fixed cost = Total Cost when volume is zero. Note that in
the real world fixed costs can rise as you gear up to meet customer
demand, but this number has to be constant (20) to solve this problem.
TVC: total variable cost = total cost for the last increment in
production. It's easy here because output increases by 10 each time,
so it's (TCn - TCn-1)/10, where n is the latest Total Cost row; n-1
is the previous Total Cost row.
AFC: average fixed cost = Fixed Cost/# units Output; with constant
fixed costs this will decline with each unit
AVC: average variable cost = (Total Cost - Fixed Cost)/# units of
Output; in a spreadsheet it's simply (Column 2 - 20)/Column 1
ATC: average total cost = # units of Output/Total Cost; Column
2/Column 1
MC: marginal cost = change in Total Cost to produce the last 10 units;
or for the first units, (COL2, ROW2 - COL2, ROW1)/10
Here are the numbers:
Output TC TFC TVC AFC AVC ATC MC
0 20 20 0 NA NA NA NA
10 40 20 20 2.00 2.00 4.00 2.00
20 60 20 40 1.00 2.00 3.00 2.00
30 90 20 70 .67 2.33 3.00 3.00
40 120 20 100 .50 2.50 3.00 3.00
50 180 20 160 .40 3.20 3.60 6.00
60 280 20 280 .33 4.33 4.67 10.00
This format doesn't permit graphing but a spreadsheet could quickly
produce a chart of ATC and MC. This ATC is U-shaped because initially
it costs only $20 to produce another 10 units and the fixed costs are
declining. Then, something's causing the marginal cost to go up
faster than the fixed costs per unit are declining. To get the last
10 units (between 50 and 60), adds $100 or $10 per unit. Yikes -- get
after the production manager!
It's not what one would expect to see with "economies of scale" but is
the case in this exercise! |
