Find the producers' surplus if the supply function for pork bellies is given by the following. S(q) = q^5/2 + 2q^3/2 + 53 | Homework.Study.com (2024)

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Business Economics Economic surplus

Question:

Find the producers' surplus if the supply function for pork bellies is given by the following.

{eq}S(q) = q^{\frac{5}{2}} + 2q^{\frac{3}{2}} + 53{/eq}

Assume supply and demand are in equilibrium at {eq}q = 9{/eq}.

Producers' Surplus:

  • If a producer want to sell his product at a price which is less than the price offered to him, and the buyer want to give him extra money than the demanded by the producer, the producers is going to have a surplus profit. The sam of all the surplus profits gained by a producer is known as the producers' surplus.
  • We can apply the following formula to find the Producers' surplus:

$$\begin{align}\hspace{1cm}\ S_{\text{Producer}}^{\text{surplus}} = \int (P_{\text{Indicated/equilibrium}}^{Price}- \text{Supply}^{Price} )\ \text{d}x \\[0.3cm]\hspace{1cm}\frac{dc}{dx} &=0 & \left[\text{ Where c is constant value } \right]\\[0.3cm]\hspace{1cm}\displaystyle \frac{d}{dx}x^n &=nx^{n-1} & \left[\text{ This is power rule of differentiation } \right]\\[0.3cm]\end{align} \\$$

Answer and Explanation:1

Given Data

$$\begin{align}S(q) &= q^{\frac{5}{2}} + 2q^{\frac{3}{2}} + 53\\[0.3cm]q &= 9\\[0.3cm]\end{align} \\$$

The producer's surplus is...

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