Consumer Surplus question

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.

Answer 1

Image courtesy http://economicsonline.co.uk/

Consumer surplus is the sum (integral) of differences between the price each consumer would have payed and the price they got to pay. You need to find out the area of the green zone on the above graph, in the case of your model.

Answer 2

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: $$\begin{align*}\Delta CS&=& \int_{P_1^*}^{P_0^*}Q(P)\text{dP}\\ \end{align*}$$