Question

Suppose a perfectly competitive market has the following inverse supply and demand curves: Supply: P= 5+2Q Demand: P = 50-Q.

1) Solve for the perfectly competitive Pe and Qe, and calculate consumer+producer surplus at Pe, Qe.

Answer #1

As per the question a perfectly competitive market has

The inverse supply function is P= 5 +2Q therefore the supply choke price is = 5

P -5 =2Q or 2Q=P-5

Q= 0.5P -2.5

The inverse demand function is P= 50 - Q therefore the demand choke price is = 50

P= 50 – Q or Q= 50- P

Perfectly competitive market attains equilibrium when quantity demand = quantity supply

0.5P -2.5 = 50- P

1.5P = 52.5

P=52.5/1.5 = 35 therefore Equilibrium Price (Pe) = 35

By replacing the P=35, then Q= 50- P = 50 -35 = 15 therefore Equilibrium quantity (Qe) = 15

Consumer Surplus = 0.5(50-35)(15-0) = 0.5x15x15 = 112.5

Producer Surplus = 0.5(35-5)(15-0) = 0.5x30x15 = 225

Total surplus = Consumer surplus + Producer surplus = 112.5 +225 = 337.5

In the below diagram the horizontal axis represents the quantity and the vertical axis represents the price, the equilibrium point is E where the market demand equals with the market supply. Therefore the equilibrium price is 35 and equilibrium quantity is 15

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