Question

The supply function of a product is p = 0.4e^2x, where x denotes 1000 units. Find producer's surplus when sales are 2000 units.

Answer 1

Given:

The supply function of a product is p₀ = 0.4e^2x, where x denotes 1000 units.

To Find:

The producer's surplus when sales are 2000 units.

Solution:

We have been given that the supply function of a product is p = 0.4e^2x, where x denotes 1000 units.

We need to find the producer's surplus p₀ when sales are 2000 units, i.e.

The producer's surplus p₀ when sales are 2000 units

\(= x_0 p_0 - 0.4 \int\limits_0^2 e^{2x}dx\)

\(= 2 \times 21.84 -[0.2(e^4 - e^0)]\)

\(= 32.96\)

∴ The producer's surplus p₀ when sales are 2000 units is 32.96 units.