Question

9. In this definite integral problem, p is in dollars and x is the number of units. If the demand function for a product is p = 28/(x + 1) and the supply function is p = 1 + 0. 2x, find the consumer's surplus under pure competition. (Round your answer to two decimal places. ) ​

Answer 1

The consumer's surplus under pure competition is  3.005

The demand function for product p = 28/(x + 1)  and the supply function p= 1 + 0. 2x,

the equilibrium points are p and x

p = 28/(x + 1),p=1 + 0. 2x,

to calculate equilibrium points just equal both p functions,

28/(x + 1)=1 + 0. 2x,

28=(1+0.2x)*(1+x),

28=1+1.2x+0.2$x^{2}$,

0.2$x^{2}$+1.2x-27=0,

by using quadratic equation formula,

$x=-b+\sqrt{b^{2}-4ac } /2a$,

$x=-1.2+\sqrt{1.2^{2}-4*0.2*27} /2*0.2$,

x=-1.2+4.86/0.4,

x=9.15,

p = 28/(x + 1),

p=28/9.15+1,

p=28/10.15,

p=2.75,

the equilibrium points are x=9.15,p=2.75,

The consumer surplus is

$\int\limits^x_0 {p} \, dx -p*x$

$\int\limits^x_0 {28/x+1} \, dx-9.15*2.75$

=$\left \{ {{x=9.15} \atop {x=0}} \right.$28(log(x+1))-25.1625

=3.005

The consumer surplus is 3.005

To solve more questions about consumer's surplus:

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