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.