Answer to Question #212569 in Calculus for Akhona Klanisi

Question

Question  14

The supply function of a good is given by

P_s = Q² − 2Q + 12.

Determine the producer surplus if ten units are supplied (Q = 10) at price P.

 

[1.     353,33

[2.     686,67

[3.     566,67

[4.     1273,33

Answer 1

$\text{First, we calculate the equilibrium price using at Q = 10 which is the equilibrium}\\\text{Therefore, } P = 10^2-2(10)+12=92\\\text{Our production surplus is given by}\\PQ-\int_{0}^{10}(Q^2-2Q+12)dQ \\=920-[\frac{Q^3}{3}-Q^2+12Q]_{0}^{10}\\=566.67$