# Consumer Surplus question

The demand for rail travel is $Q^d = 600 - 2P$ where quantity is thousands of train journeys per quarter and $P$ is in £ per journey. How much would the consumer surplus change if rising cost of electricity led the train companies to raise price from £70 to £100.

Calculating the choke price, $600 = 2P$. Thefore $P = 300$.

At £70, $Q^d = 460$. Therefore Consumer surplus is $(460-300)/2*460 = £36,800$

At £100, $Q^d = 400$. Therefore consumer surplus is $(400-300)/2*400 = £20,000$

Difference is $£16,800$.

I've got the answer wrong, but i'm sure where, any help is appreciated.

Given the demand function: $$Q(P)=600-2P$$ The consumer surplus is the area under the demand curve above the equilibrium price $P^*$ or algebraically; $$\int_{0}^{P^*}Q(P)\text{dP}$$ The change in consumer surplus as a result of price change from $P_0^*$ to $P_1^*$ is then: \begin{align*}\Delta CS&=& \int_{P_1^*}^{P_0^*}Q(P)\text{dP}\\ \end{align*}