AS Level Economics 9708: Consumer Surplus, Producer Surplus and a Demand Shift

A farmers' market stallholder sells jars of organic honey each week. The market demand and supply for organic honey jars can be modelled by the following equations, where $P$ is the price in dollars per jar and $Q$ is the quantity of jars per week:

$P_d = 20 - 0.1Q$ $P_s = 2 + 0.05Q$

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

(b) Calculate the consumer surplus and the producer surplus at this equilibrium, showing your working. [3]

(c) A health-food trend then increases demand for organic honey, and with supply unchanged the demand equation becomes $P_d' = 26 - 0.1Q$ . Calculate the new equilibrium price and quantity, and the new consumer surplus and producer surplus. [4]

Part (a): The original equilibrium

At equilibrium, the price on the demand curve equals the price on the supply curve, $P_d = P_s$ : $20 - 0.1Q = 2 + 0.05Q$

Collecting terms: $20 - 2 = 0.05Q + 0.1Q$ $18 = 0.15Q$ $Q = 120 \text{ jars per week}$

Substituting back into the demand equation: $P = 20 - 0.1(120) = 20 - 12 = 8$

Checking against the supply equation: $P_s = 2 + 0.05(120) = 2 + 6 = 8$ . Both agree, confirming the equilibrium.

So the original equilibrium is a price of $8 and a quantity of 120 jars per week.

Part (b): Consumer surplus and producer surplus at equilibrium

Consumer surplus is the area of the triangle between the demand curve and the equilibrium price, from $Q=0$ to $Q=120$ . Its height is the gap between the demand curve’s price-intercept (the price at $Q=0$ , here $20. The most a buyer would pay for a single jar) and the equilibrium price of $8: $CS = \frac{1}{2}\times(20-8)\times120 = \frac{1}{2}\times12\times120 = 720 \text{ per week}$

Producer surplus is the area of the triangle between the equilibrium price and the supply curve, from $Q=0$ to $Q=120$ . Its height is the gap between the equilibrium price of $8 and the supply curve’s price-intercept (the price at $Q=0$ , here $2. The minimum price needed before any jars are supplied at all): $PS = \frac{1}{2}\times(8-2)\times120 = \frac{1}{2}\times6\times120 = 360 \text{ per week}$

Part (c): The new equilibrium and surplus after the demand shift

The health-food trend raises demand at every price, so the demand curve’s price-intercept rises from $20 to $26 (buyers are now willing to pay more for a given quantity). Setting the new demand price equal to the (unchanged) supply price, $P_d' = P_s$ : $26 - 0.1Q = 2 + 0.05Q$ $26 - 2 = 0.15Q$ $24 = 0.15Q$ $Q = 160 \text{ jars per week}$

Substituting back: $P = 26 - 0.1(160) = 26 - 16 = 10$

Checking against supply: $P_s = 2 + 0.05(160) = 2 + 8 = 10$ . Both agree.

So the new equilibrium is a price of $10 and a quantity of 160 jars per week.

New consumer surplus, using the new price-intercept of $26: $CS' = \frac{1}{2}\times(26-10)\times160 = \frac{1}{2}\times16\times160 = 1{,}280 \text{ per week}$

New producer surplus, using the unchanged supply price-intercept of $2: $PS' = \frac{1}{2}\times(10-2)\times160 = \frac{1}{2}\times8\times160 = 640 \text{ per week}$

Both consumer surplus ($720 → $1,280) and producer surplus ($360 → $640) rise as a result of the rightward shift in demand: buyers now demand more at every price, which pulls the equilibrium to a higher price and a larger quantity, expanding the area of both triangles.

Final answers

(a) Original equilibrium: price $=$ $8, quantity $=$ 120 jars per week.
(b) Consumer surplus $=$ $720 per week; producer surplus $=$ $360 per week.
(c) New equilibrium: price $=$ $10, quantity $=$ 160 jars per week. New consumer surplus $=$ $1,280 per week; new producer surplus $=$ $640 per week, both rise following the increase in demand.