Question

suppose the market for cell phones can be responsible by the following demand and supply equation
Q = 300-3/2p Q=5/2p-200

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find the free market equilibrium price, equilibrium quantity, consumer surplus,producer surplus and total surplus

Answer 1

1. At equilibrium, quantity supplied= quantity demanded.

Thus, 300-3/2p =5/2p-200

300+ 200= 5/2p + 3/2p

500= 8/2p or 500 =4p

500/4=p or 125=p

Putting P=125 to find quantity: Q=  300-3/2(125) = 300-187.5 = 112.5

Thus the free market equilibrium price is $125 and equilibrium quantity is 112.5 units.

2. To find intercept on y axis of demand and supply curves, we have to rearrange the Qd and Qs equations in the form of P.

That is, Qd= 300-3/2p can be rearranged as P= 200 - 2/3q

Qs= 5/2p-200 can be rearranged as P= 80 + 2/5q

Consumer Surplus (CS) is the area under the demand curve and above the equilibrium price. It can be calculated using the formula for area of a triangle= 1/2 x base x height.

CS= 1/2 x 112.5 x (200-125) = $ 4218.75

Produer Surplus (PS) is the area under the equilibrium price and above the supply curve.

PS= 1/2 x 112.5 x (125 - 80) = $ 2531.25

3. Total Surplus= consumer surplus + producer surplus

Total Surplus= $ 4218.75 + $ 2531.25

Total Surplus= $6750