Hearthside Furniture makes bespoke wooden garden benches in a single workshop with a fixed number of woodworking machines. In the short run, only the number of workers it employs can vary. Total fixed cost is $60 per week. The table shows total variable cost (TVC) at different w…

Answer: ((a)) Marginal cost of the 4th bench =124-108=16 (i.e. $16) and marginal cost of the 5th bench =150-124=26 (i.e. $26) ((b)) Average cost at 3 benches =108÷3=36 (i.e. $36) and average cost at 6 benches =186÷6=31 (i.e. $31) ((c)) Marginal cost is lowest at an output of 3 benches per week ($12); beyond this output, each additional worker adds less extra output than the last (diminishing marginal returns to the fixed workshop and machines), so each extra bench needs more extra variable cost to produce, pus… ((d)) Average cost is lowest at an output of 5 benches per week ($30); average cost keeps falling as long as marginal cost is below it, and only starts rising once marginal cost has risen above it, which happens between 5 and 6 benches in this table. Setting up the full cost table Total cost (TC) = total fixed cost (TFC) + total variable cost (TVC), with TFC = $60 at every output: Output 0 1 2 3 4 5 6 TVC ($) 0 20 36 48 64 90 126 TC ($) 60 80 96 108 124 150 186 Part (a): Marginal cost…

A Level Economics 9708: Short-Run Marginal Cost and Average Cost

Output (benches per week)

TVC ($)

126

Setting up the full cost table

Total cost (TC) $=$ total fixed cost (TFC) $+$ total variable cost (TVC), with TFC $=$ $60 at every output:

Output	0	1	2	3	4	5	6
TVC ($)	0	20	36	48	64	90	126
TC ($)	60	80	96	108	124	150	186

Part (a): Marginal cost of the 4th and 5th benches

Marginal cost (MC) is the change in total cost from producing one more unit:

$MC(\text{4th bench}) = TC(4) - TC(3) = 124 - 108 = 16$

This is $16.

$MC(\text{5th bench}) = TC(5) - TC(4) = 150 - 124 = 26$

This is $26.

Part (b): Average cost at 3 and 6 benches

Average cost (AC) $=$ TC $\div$ Q:

$AC(3) = \frac{108}{3} = 36$

This is $36.

$AC(6) = \frac{186}{6} = 31$

This is $31.

Part (c): Where marginal cost is lowest, and why it rises again

Computing MC at every output from the table above:

Output	1	2	3	4	5	6
MC ($)	20	16	12	16	26	36

Marginal cost is lowest at an output of 3 benches per week, at $12.

Beyond this output, marginal cost rises again ($16, $26, $36) because of the law of diminishing returns: with the number of machines and the size of the workshop fixed in the short run, adding more workers to this fixed capital eventually means each additional worker contributes less extra output (a falling marginal product of labour) than the worker before. Since each extra worker still costs the same in wages, producing that smaller amount of extra output costs progressively more per extra bench, so marginal cost rises.

Part (d): Where average cost is lowest, and its relationship with marginal cost

Computing AC at every output:

Output	1	2	3	4	5	6
AC ($)	80	48	36	31	30	31

Average cost is lowest at an output of 5 benches per week, at $30.

Marginal cost is below average cost at every output up to 5 benches (for example, the marginal cost of the 5th bench ($26) is still less than the average cost at that output ($30)) and a marginal cost below average cost continues to pull average cost down. Once marginal cost rises above average cost, the marginal cost of the 6th bench ($36) exceeds the average cost of $31 at that output, average cost is pulled back up instead. This is why average cost falls only as long as marginal cost sits below it, and why its minimum occurs at the output where marginal cost has just risen to meet, or pass, it.

Final answers

(a) MC of the 4th bench $=$ $16; MC of the 5th bench $=$ $26
(b) AC at 3 benches $=$ $36; AC at 6 benches $=$ $31
(c) Marginal cost is lowest at 3 benches per week; it rises again afterwards because of diminishing returns to the fixed workshop and machines as more workers are added
(d) Average cost is lowest at 5 benches per week, because average cost falls while marginal cost is below it and rises once marginal cost moves above it