Consumer and producer surplus

Consumer and producer surplus

Lessons

Let S(q)S(q) and D(q)D(q) be supply and demand curves in terms of qq, where qq is the quantity.

Then we calculate the producer and consumer surplus by using the following formulas:

PSPS (producer surplus) = 0q[pS(q)]dq\int_{0}^{\overline q} [\overline p - S(q)] dq

CSCS (consumer surplus) = 0q[D(q)p]dq\int_{0}^{\overline q} [D(q) - \overline p] dq

Where p\overline p and q\overline q are equilibrium prices and quantity.

  • Introduction
    Consumer and Producer Surplus Overview:
    a)
    Review of Consumer and Producer Surplus

    b)
    Evaluating Surplus with Integrals


  • 1.
    Calculating Producer and Consumer Surplus

    The demand curve for cakes is given by D(q)=362q2D(q) = 36 - 2q^{2} and the supply curve is given by S(q)=8q+12S(q) = 8q + 12.

    i)Find the producer surplus

    ii)Find the consumer surplus


  • 2.

    The demand curve for cakes is given by D(q)=12q+2D(q) = \frac{12}{q + 2} and the supply curve is given by S(q)=q+3S(q) = q + 3.

    i)Find the producer surplus

    ii)Find the consumer surplus