Question

The demand function is p = 100/q and an increase in price reduces quantity demanded from q = 10 to q =5. Compute the lost consumer surplus (CS). First draw a diagram that illustrates the lost CS. Then integrate with respect to 𝑝 (the variable on the vertical axis) after finding

(1) the inverse demand function , 𝑞 =𝑓 (𝑝) and

(2) the endpoints of integration (corresponding to q = 10 to q = 5 ) on the

𝑝 axis .

Answer 1

 Diagram that illustrates the lost CS

Given P =20 and q = 5 ; When P=10 q = 10

So change in in CS $= ∫^{10}_{5} 100q^{-1}\delta q$

$= 100ln(q) ⌈^{10}_{5} = -100(ln(10)-ln(5)) =100(ln(2))$

 

inverting the demand function we get $q=\frac{100}{p}$

the integral then becomes;

$∫^{10}_{5}\frac{100}{p} = 100(ln20 -ln10) = -100ln(2)$