Saved Bookmarks
| 1. |
Find the consumer's surplus for the demand function \( p=10-x-x^{2} \) and the supply function is \( p=x+2 \) at an equilibrium. |
|
Answer» Given that Pd = 10 - x - x2----(1) and Ps = x + 2---(2) On equilibrium, we have Pd = Ps ⇒ 10 - x - x2 = x + 2 ⇒ x2 + 2x - 8 = 0 ⇒ (x + 4) (x - 2) = 0 ⇒ (x + 4) (x - 2) = 0 ⇒ x = 2, -4 \(\therefore\) x = 2 (\(\because\) x never be negative) Put x = 2 in equation (1) we get (Pd)2 = 10- 2 - 22 = 10 - 2 - 4 = 10 - 6 = 4 Now consumer's surplus = \(\int\limits_0^2(10-x-x^2)dx-2\times4\) = \([10x-\frac{x^2}2-\frac{x^3}3]_0^2-8\) = 20 - 2 - 8/3 - 8 = 10 - 8/3 = \(\frac{30-8}3=\frac{22}3\) |
|