So I have a demand function:
$$D(p)=A-ap$$
And I've found $\frac{d}{dp} CS$ which is $-D(p)=-(A-ap)=-A+ap$.
I'm not sure what to conclude, but I've said that "More products sold will result in a rise in prices." I'm concluding this because when i illustrate the $\frac{d}{dp} CS=-D(p)$, it shows just that.
Can anybody please confirm or deny? I'm kinda lost.
If consumers pay a price $p$, consumer surplus is
$$CS(p)=\int_p^\infty D(\tilde p)d\tilde p $$,
which captures the monetary gain afforded to consumers due to the gap between what they are willing to pay and what they actually pay.
So $\partial_p CS(p)=-D(p).$ This tells us roughly that for every unit increase in the price, the CS drops by the amount demanded.
This makes sense since consumers buy less as the price goes up and thus enjoy less welfare.