AS Level Economics 9708: Equilibrium from Demand and Supply Functions, and a Supply Shift

A stationery retailer's monthly market for a particular style of hardback notebook can be modelled with the following demand and supply functions, where $P$ is the price in dollars and $Q$ is the quantity of notebooks per month:

$Q_d = 1000 - 40P$ $Q_s = 200 + 60P$

(a) Using these functions, calculate the equilibrium price and quantity of notebooks, showing your working. [3]

(b) The government then introduces a new environmental compliance cost on notebook production. With demand unchanged, the market's supply function becomes $Q_s' = 100 + 60P$ . Explain why this change represents a shift of the supply curve rather than a movement along it, and state the direction of the shift. [3]

(c) Using the new supply function $Q_s'$ , calculate the new equilibrium price and quantity, and describe the overall change in equilibrium price and quantity compared with your answer to (a). [4]

Part (a): The original equilibrium

At equilibrium, quantity demanded equals quantity supplied, $Q_d = Q_s$ : $1000 - 40P = 200 + 60P$

Collecting the $P$ terms on one side and the constants on the other: $1000 - 200 = 60P + 40P$ $800 = 100P$ $P = 8$

Substituting $P=8$ back into the demand function to find equilibrium quantity: $Q = 1000 - 40(8) = 1000 - 320 = 680$

Checking against the supply function: $Q_s = 200 + 60(8) = 200 + 480 = 680$ . Both give the same quantity, confirming the equilibrium.

So the original equilibrium is a price of $8 and a quantity of 680 notebooks per month.

Part (b): Why this is a shift, and its direction

The new environmental compliance cost raises the retailer’s cost of producing each notebook. A change in a cost of production is a non-price determinant of supply, so it changes the entire relationship between price and quantity supplied. It shifts the whole supply curve. It is not a movement along the curve, because nothing has directly changed the notebook’s own selling price $P$ itself; that price is only determined afterwards, at the new equilibrium.

To find the direction, compare the two supply functions at the same price $P$ : the original function gives $Q_s = 200+60P$ , while the new function gives $Q_s' = 100+60P$ . Since $100+60P$ is always $100$ less than $200+60P$ for any given $P$ , a smaller quantity is now supplied at every price. This means the supply curve shifts left (supply decreases).

Part (c): The new equilibrium and the overall change

At the new equilibrium, $Q_d = Q_s'$ : $1000 - 40P = 100 + 60P$ $1000 - 100 = 100P$ $900 = 100P$ $P = 9$

Substituting $P=9$ back into the demand function: $Q = 1000 - 40(9) = 1000 - 360 = 640$

Checking against the new supply function: $Q_s' = 100 + 60(9) = 100 + 540 = 640$ . Both agree, confirming the new equilibrium.

So the new equilibrium is a price of $9 and a quantity of 640 notebooks per month.

Comparing the two equilibria:

Equilibrium price rises, from $8 to $9.
Equilibrium quantity falls, from 680 to 640 notebooks per month.

This is exactly what is expected from a leftward shift of the supply curve with demand unchanged: with fewer notebooks willing to be supplied at every price, buyers must move up the (unchanged) demand curve, so price rises and quantity falls.

Final answers

(a) Original equilibrium: price $=$ $8, quantity $=$ 680 notebooks per month.
(b) The supply curve shifts left (supply decreases), because the compliance cost changes the cost of producing at every price, not the notebook’s own selling price.
(c) New equilibrium: price $=$ $9, quantity $=$ 640 notebooks per month. Overall, equilibrium price rises and equilibrium quantity falls.