IGCSE Economics 0455: PES in the Short Run and Long Run for a Furniture Workshop

A small furniture workshop makes handmade wooden dining tables. It raises the price of a table from $300 to $360.

In the short run (the first month after the price rise, before the workshop can hire more staff or expand its premises) the quantity of tables it supplies rises from 40 to 44 per month.

In the long run (one year after the price rise, once the workshop has hired two more carpenters and expanded into a larger workshop) the quantity of tables it supplies is 60 per month, compared with the original 40 per month.

(a) Calculate the price elasticity of supply (PES) of dining tables in the short run. [3]

(b) Calculate the price elasticity of supply (PES) of dining tables in the long run. [3]

(c) Using your answers to (a) and (b), explain why the price elasticity of supply of dining tables is higher in the long run than in the short run. [3]

Part (a): Short-run PES

Percentage change in price (this is the same in both parts, since the price change is the same): $\%\Delta P = \frac{360-300}{300}\times100 = \frac{60}{300}\times100 = +20\%$

Percentage change in quantity supplied in the short run, using the original quantity of 40 as the base: $\%\Delta Q_s^{SR} = \frac{44-40}{40}\times100 = +10\%$

$PES_{SR} = \frac{10}{20} = 0.5$

Since $0.5 < 1$ , short-run supply is price inelastic.

Part (b): Long-run PES

The percentage change in price is unchanged at $+20\%$ . Percentage change in quantity supplied in the long run, again measured from the original quantity of 40 (not the short-run figure of 44): $\%\Delta Q_s^{LR} = \frac{60-40}{40}\times100 = +50\%$

$PES_{LR} = \frac{50}{20} = 2.5$

Since $2.5 > 1$ , long-run supply is price elastic.

Part (c): Why long-run supply is more elastic

In the short run, the workshop’s staff, tools and workshop space are fixed, so it can only squeeze out a small extra quantity of tables (a rise from 40 to 44) even though the price has risen by 20%. This gives the low, inelastic value of $PES_{SR} = 0.5$ .

Given a full year, however, the workshop can hire two more carpenters, buy in more raw materials and move into a larger workshop. With these extra resources, it can raise output much further (from 40 to 60 tables per month), giving the higher, elastic value of $PES_{LR} = 2.5$ . The general principle is that the longer the time period producers have to adjust their inputs, the more they are able to change output in response to a price change, so price elasticity of supply rises as the time period lengthens.

Final answers

(a) $PES_{SR} = 0.5$ . Short-run supply is price inelastic
(b) $PES_{LR} = 2.5$ . Long-run supply is price elastic
(c) Supply becomes more elastic over time because firms can hire more workers, buy more materials and expand capacity the longer they have to adjust, so a longer time period allows a proportionately larger response in quantity supplied