Question

How to find producer's surplus at the market equilibrium point if supply function is ?

Answer 1

Find equilibrium price `p_e` and quantity `x_e` then evaluate `int_0^(x_e) (p_e-(0.8x+18)) dx`

Explanation:

The producers surplus can be thought of as the area between the horizontal line at the equilibrium price and the supply curve from `0` to the equilibrium quantity.

In this problem solve `0.8x+18 = 554.4/(x+13` to get equilibrium quantity `x=9` whatever quantity units we are working in, tons, thousand items, bushels, whatever.
(Note that: we reject the quantity solution `x=-44.5`).

At this quantity we find the price is `25.2` whatever monetary unit we are working in, dollars, thousand dollars, Yen, whatever.

So the producers surplus is

`int_0^9 (25.2-(0.8x+18))dx = 32.4` monetary units.