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 .
Diagram that illustrates the lost CS
Given P =20 and q = 5 ; When P=10 q = 10
So change in in CS "= \u222b^{10}_{5} 100q^{-1}\\delta q"
"= 100ln(q) \u2308^{10}_{5} = -100(ln(10)-ln(5)) =100(ln(2))"
inverting the demand function we get "q=\\frac{100}{p}"
the integral then becomes;
"\u222b^{10}_{5}\\frac{100}{p} = 100(ln20 -ln10) = -100ln(2)"
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