Inverse function of market demand for certain good is equal to $P=100-0.25Q$, inverse supply function is $P=20+0.55Q$. Calculate equilibrium price and quantity. Furthermore calculate consumer and producer surplus.

Equlibrium price and quantity i think i know how to calculate: $$20+0.55Q=100-0.25Q$$ and this will be the quantity whereas the price will be (substituting Q with value calculated above): 20+0.55Q=P am i correct with this? I am lost with consumer/producer surplus need more help. edit: I have and idea about consumer/producer surplus: consumer: $0.5 \times 100 \times 25=1250$ and producer $100 \times 55 \times 0.5=2750$ is this correct?

  • 1
    $\begingroup$ When you are lucky enough to deal with affine/linear functions, it is a pity not to draw diagrams, to see for your eyes consumer and producer surplus, before calculating numerical values. $\endgroup$ Apr 8, 2015 at 19:56
  • $\begingroup$ but am i right or wrong with my solutions? $\endgroup$
    – Krowskir
    Apr 9, 2015 at 11:30
  • $\begingroup$ The price and quantity are obviously correct. For the surpluses I don't know -draw the diagrams and you will figure it out. $\endgroup$ Apr 9, 2015 at 12:37
  • $\begingroup$ I have the diagram and what i have calculated is the area of those two triangles that on the graph should represent consumer and producer surplus. Nevertheless thank you for your answer. $\endgroup$
    – Krowskir
    Apr 9, 2015 at 13:09

1 Answer 1


Equating supply and demand we obtain the equilibrium

$$P^* = 75, Q^*=100$$

The corresponding diagram is enter image description here

Consumer Surplus is the area of triangle $B-E-C$ so

$$CS = \frac 12 \cdot (100-75)\cdot 100 = 1250$$

Producer Surplus is the area of the triangle $B-E-A$ so

$$PS = \frac 12 \cdot (75-20)\cdot 100 = 2750$$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.