Question

Consider three Perfectly Competitive market scenarios. The market demand curve is given by P = 100 – Q where P is the market price and Q is the market quantity. In the first scenario, the market supply function is P = $50. In the second, the market supply function is P = Q, and in the third, the market supply function is Q = 50.

For each scenario, draw the appropriate graph; then calculate the equilibrium price and quantity, the total Consumer Surplus, and the total Producer Surplus.   Finally, briefly explain what is happening to the total Producer Surplus as you go from the first to the second to the third scenario. More importantly, explain why this is happening. The best answers will be framed in terms of an elasticity.

Answer 1

P = 100 - Q

Q = 100 - P

(a) Market supply: P = 50

Equating with market demand function,

100 - Q = 50

Q = 50

P = 50

From demand function,

When Q = 0, P = $100 (Vertical intercept)

When P = 0, Q = 100 (Horizontal intercept)

In following graph, AB & CD are market demand & supply curves intersecting at point E with equilibrium price P0 (= $50) and quantity Q0 (= 50).

Consumer surplus (CS) = Area between demand curve & equilibrium price = Area AEP0 = (1/2) x $(100 - 50) x 50

= 25 x $50 = $1,250

Producer surplus (PS) = Area between supply curve & equilibrium price = Zero (Since Market supply = Price).

(b) Market supply: P = Q

Equating with market demand,

100 - Q = Q

2Q = 100

Q = 50

P = Q = 50

From supply function, when Q = 0, P = 0 (i.e. Supply function is a straight line from origin)

In following graph, AB & CD are market demand & supply curves intersecting at point E with equilibrium price P0 (= $50) and quantity Q0 (= 50).

Consumer surplus (CS) = Area AEP0 = (1/2) x $(100 - 50) x 50 = 25 x $50 = $1,250

Producer surplus (PS) = Area CEP0 = (1/2) x $(50 - 0) x 50 = 25 x $50 = $1,250

(c) Market supply: Q = 50

Equating with market demand,

100 - P = 50

P = 50

Q = 50

In following graph, AB & CD are market demand & supply curves intersecting at point E with equilibrium price P0 (= $50) and quantity Q0 (= 50).

Consumer surplus (CS) = Area AEP0 = (1/2) x $(100 - 50) x 50 = 25 x $50 = $1,250

Producer surplus (PS) = Area 0CEP0 = $(50 - 0) x 50 = $2,500

(d) As we move from first to third scenario, producer surplus continues to increase from $0 to $2,500. This is because in first scenario, market supply is horizontal, therefore market supply is perfectly elastic and PS is minimized (= zero), while in third scenario, market supply is vertical, therefore market supply is perfectly inelastic and PS is maximized (= $2,500). As supply becomes less elastic, PS increases.