The producer's surplus when the supply function for a commodity is $p = 3 + x$ and $x_0 = 3$ is ______. (a) $\frac{3}{2}$ (b) $\frac{5}{2}$ (c) $\frac{7}{2}$ (d) $\frac{9}{2}$

The producer's surplus when the supply function for a commodity is p = 3 + x and x₀ = 3 is ___. (a) (3)/(2) (b

Question 18 of 42

p = 3 + x

(a)

\frac{3}{2}

(b)

\frac{5}{2}

(c)

\frac{7}{2}

(d)

\frac{9}{2}

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Producer's surplus $= \dfrac{9}{2}$ .

The supply function is $p = 3 + x$ and $x_0 = 3$ . First find the market price at $x_0$ :

$p_0 = 3 + 3 = 6.$

Producer's surplus is

$PS = p_0 x_0 - \int_0^{x_0} (\text{supply})\,dx = 6\cdot 3 - \int_0^{3} (3+x)\,dx.$

Evaluate the integral:

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