Answer to Question #212558 in Calculus for Akhona Klanisi

Question

Question  7

Calculate the consumer surplus for the demand function

P = 25/ Q + 2

when the market price P = 5.

 

1.      2,3

2.      15,0

3.      7,9

4.      25,2

Answer 1

Market price is an equilibrium point between p and q at that moment. So q^*=25/(p^*-2)=25/3=8.3

The consumer surplus is:

$\int^{q{^*}}_0d(q)dq-p^*q^*=\int^{q{^*}}_0(25/Q+2)dq-p^*q^*=25ln(Q)+2Q|^{q{^*}}_0-p^*q^*=25ln(q^*)+2q^*-p^*q^*=52.9+16.6-41.5=28$

Answer: 28