Question

The demand function for orange juice is q = 269 - 9p and the supply function is q = 9 + 4p, where q is the number of units sold per year and p is the price per unit, expressed in dollars. The government decides to support the price of orange juice at a price floor of $24 per unit by buying orange juice and destroying all that it has purchased. How many units must the government destroy per year?

Answer 1

Answer: The government must destroy 52 units.

Explanation:

For the price floor be supported, we cannot have a demand higher than the supply (price will go up) and cannot have supply higher than demand (price will go down).

Demand = supply keep the price floor.

The government will have to purchase or destroy the excess supply.

p = 24

qd = 269 - 9p

qd = 269 - 9.24 = 53

qs = 9 + 4p

qs = 9 + 4.24 = 105

qd = qs

105 - 53 = 52

The government must destroy 52 units.