In a purely competitive market, the price of a good is naturally driven to the v

Question

In a purely competitive market, the price of a good is naturally driven to the value where the quantity demanded by consumers matches the quantity made by producers, and the market is said to be in equilibrium. These values are the coordinates of the point of intersection of the supply and demand curves. Given the demand curve p - 60 - x and the supply curve p = 30 + 1/15 x for a good, at what quantity and price is the market for the good in equilibrium? Find the consumer surplus and the producer surplus when the market is in equilibrium. Illustrate by sketching the supply and demand curves and identifying the surpluses as areas.

Explanation / Answer

Demand p = 60 - x/30 , supply p = 30 + x/15

equilibrium ==> 60 - x/30 = 30 + x/15

==> 60 - 30 = x/30 + x/15

==> 30 = x/10

==> x = 300

equlibrium quantity = 300

pe = 60 - 300/30 = 50

Hence equilibrium price pe = $50

b) Consumer surplus = [0 to 300] Demand - equilibrium price d x

==> Consumer surplus = [0 to 300] 60 - x/30 - 50 dx

==> Consumer surplus = [0 to 300] 10x - x2/30(2)   ; since xn dx = xn+1/(n +1)

==> Consumer surplus = [(10(300) - (300)2/60) - (10(0) - (0)2/60)]

==> Consumer surplus = $1500

Producer surplus = [0 to 300] equilibrium price - supply dx

==> Producer surplus = [0 to 300] 50 - (30 + x/15) dx

==> Producer surplus = [0 to 300] 20 - x/15 dx

==> Producer surplus = [0 to 300] 20x - x2/15(2)   ; since xn dx = xn+1/(n +1)

==> Producer surplus = [(20(300) - (300)2/30) - (20(0) - (0)2/30)]

==> Producer surplus = $3000

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