math and economics

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. Notice that you could integrate with respect to either 𝑞 or 𝑝 (in the latter case, after finding the inverse demand function, 𝑞 = 𝑓(𝑝) and writing the endpoints in terms of 𝑝).

Answer 1

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

So Changin in CS - = ∫₅¹⁰ 100q^-1dq

= 100ln(q) ⌈₅¹⁰ = -100(ln(10)-ln(5)) =100(ln(2))

inverting we get q=100/p the intergal

becomes ∫₁₀²⁰ 100/p = 100(ln20 -ln10) = -100ln(2)

Let me know if you need any help with Mcro.

Bets, Lenny