The demand and supply functions are given by D(x)= 16 − x² and S(x) = 2x² + 4 are under perfect competition, then the equilibrium price x is ________.

(a)

2

(b)

3

(c)

4

(d)

5

The given demand and supply function are given by D(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is ________.

(a)

40

(b)

\(\frac{41}{2}\)

(c)

\(\frac{40}{3}\)

(d)

\(\frac{41}{5}\)

The profit of a function p(x) is maximum when ________.

(a)

MC − MR = 0

(b)

MC = 0

(c)

MR = 0

(d)

MC + MR = 0

The demand function for the marginal function MR = 100 − 9x² is ________.

(a)

100 − 3x²

(b)

100x − 3x²

(c)

100x − 9x²

(d)

100 + 9x²

When x₀ = 2 and P₀ = 12 the producer’s surplus for the supply function P_s = 2x² + 4 is ________.

(a)

\(\frac{31}{5}\)units

(b)

\(\frac{31}{2}\) units

(c)

\(\frac{32}{3}\) units

(d)

\(\frac{30}{7}\) units