# Equilibrium price and quantity - consumer and producer surplus

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?

• 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. – Alecos Papadopoulos Apr 8 '15 at 19:56
• but am i right or wrong with my solutions? – Krowskir Apr 9 '15 at 11:30
• The price and quantity are obviously correct. For the surpluses I don't know -draw the diagrams and you will figure it out. – Alecos Papadopoulos Apr 9 '15 at 12:37
• 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. – Krowskir Apr 9 '15 at 13:09

Equating supply and demand we obtain the equilibrium

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

The corresponding diagram is

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

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