Question

This is a question of equilibrium price and quantity.p + 2q = 20p - q = 2Using simultaneous equation formulas, I established that p = 8 and q = 6.I need to find the Consumer surplus (CS) and Producer surplus (PS)Please help me understand how to find this.

Answer 1

Given:

p + 2q = 20

p - q = 2

After solving the system of equations, we have:

p = 8

q = 6

Let's find the Consumer surplus (CS) and Producer surplus(PS).

To find the Consumer Surplus(CS), apply the formula:

$\int_0^qd(q)dq-pq$

Where;

Demand equation, dq: p + 2q = 20

p = 20 - 2q

p = 8

q = 6

Now, we have:

$\begin{gathered} [\int_0^6(20-2q)dq]-8*6 \\ \\ (20*6-20*0-2(\frac{6^2}{2}-\frac{0^2}{2}))-48 \\ \\ (120-2(18))-48 \\ \\ 84-48 \\ \\ =36 \end{gathered}$

Therefore, the Consumer Surplus is $36.

• Producer surplus:

To find the producer surplus, apply the formula:

$p*q-\int_0^qs(qs)dq$

Where:

Supply equation, qs: p - q = 2

Rewrite for p:

p = q + 2

Thus, we have:

$\begin{gathered} 8*6-\int_0^6(q+2)dq \\ \\ 48-((\frac{1}{2}*6^2+2*6)-(\frac{1}{2}*0^2+2*0)) \\ \\ 48-(\frac{36}{2}+12)-(0)) \\ \\ 48-(18+12) \\ \\ 48-30 \\ \\ =18 \end{gathered}$

Therefore, the Producer Surplus is $18.

ANSWER:

CS = $36

PS = $18