Answer to Question #235026 in Calculus for john k

Question

The demand equation for a product is $Q=10(100-p)^ 1/2$

Calculate the consumers’ surplus under equilibrium which occurs at a market price of K84. 

Answer 1

$\frac{dQ}{dp}=10(100-p)^{\frac{1}{2}}\\ =-\frac{5}{\left(100-p\right)^{\frac{1}{2}}}\\ =-\frac{5}{\left(100-84\right)^{\frac{1}{2}}}\\ =-1.25$

The negative means it is not a surplus but a deficiency