Respuesta :
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:
[tex]\int_0^qd(q)dq-pq[/tex]Where;
Demand equation, dq: p + 2q = 20
p = 20 - 2q
p = 8
q = 6
Now, we have:
[tex]\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}[/tex]Therefore, the Consumer Surplus is $36.
• Producer surplus:
To find the producer surplus, apply the formula:
[tex]p*q-\int_0^qs(qs)dq[/tex]Where:
Supply equation, qs: p - q = 2
Rewrite for p:
p = q + 2
Thus, we have:
[tex]\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}[/tex]Therefore, the Producer Surplus is $18.
ANSWER:
CS = $36
PS = $18
