Question

The demand for a commodity is given by P(Q + 1) = 231 and the supply is given by P - Q = 11 , find the consumer and produce surplus.

Answer 1

P(Q+1)=231

PQ+P= 231

$Q= \frac{231-P}{P}$

Supply

P- Q= 11

Q= P-11

At Equilibrium, $Q_s= Q_d$

$\frac{231-P}{P}= P-11$

$P^2-11P= 231-P$

$P^2-10P-231=0$

Solve for the value of P using the quadratic formula

$P= 21$

Q= 21- 11= 10

What producers are willing to sell at.

It occurs when supply intercept Q=0

P- 0= 11

$P_1= 11$

What consumers are willing to pay.

It occurs when Q= 0

P$_2$ = 231

Consumer surplus= $\frac{1}{2}\times (P_2-P_0) \times Q$

$\frac{1}{2}\times( 231-21) \times 10$ = 1050

Producer Surplus

$\frac{1}{2}\times (P_1-P_0) \times Q$

$\frac{1}{2}\times( 21-11) \times 10$ = 50