# How to Calculate Producers' Surplus for Pork Bellies Supply Function?

## What is producers' surplus and how do we calculate it?

Producers' surplus represents the difference between the amount producers are willing to supply at a given price and the price they actually receive in the market. In equilibrium, where supply and demand intersect, how is the producers' surplus calculated?

## Calculating Producers' Surplus for Pork Bellies Supply Function

The producers' surplus for the given supply function is $278.00. Producers' surplus is calculated by integrating the supply function over the range of equilibrium quantity (q = 16).

Producers' surplus is an important concept in economics that reflects the additional benefit that producers receive when selling goods at a price higher than the minimum price they are willing to accept. In this case, we are looking at the supply function for pork bellies given by S(q) = 5/2 * q^(3/2) + 4.

To calculate the producers' surplus, we first find the equilibrium price by substituting q = 16 into the supply function: S(16) = 5/2 * (16)^(3/2) + 4 = 164.

Next, we integrate the supply function from q = 16 to q = 0 to find the producers' surplus: Producers' Surplus = ∫[16, 0] (5/2 * q^(3/2) + 4) dq = 278.

Therefore, the producers' surplus for the pork bellies' supply function is $278.00. This surplus amount represents the additional benefit that producers gain from selling pork bellies at equilibrium.