Question

Suppose the demand and supply curves for sparkling cider are given by:

QD = 110 – 20P

QS = -32 + 13P

where QD is the quantity of sparkling cider demanded (in thousands of bottles), QS is the quantity supplied, and P is the price of sparkling cider (in dollars per bottle).

a. Find the equilibrium price and quantity of sparkling cider. Round P to the nearest cent (hundredth) and Q to the nearest whole number.

b.If price is set at $4 per bottle, will there be a surplus or a shortage? How large?

c.Suppose the market for sparkling cider is perfectly competitive. If a firm in this market has a marginal cost MC = 0.7 + 0.2q, how many bottles will this firm produce at the market equilibrium price?

Answer 1

a) Equilibrium occurs when demand = supply

110 - 20P = -32 + 13P

P = 4.3

At this price, Q = 23.93

b) If there is price ceiling of 4, there is quantity demanded of 30 units while quantity supplied of 20 units which creates shortage of 30 - 20 = 10 units

c) If marginal cost = 0.7 + 0.2q

Perfectly competitive firm maximize their profit when marginal revenue = marginal cost where marginal revenue is the price they receive

0.7 + 0.2q = 4.3

q = 18