Final answer:
The government-imposed price restriction of P = $40 in a perfectly competitive market results in excess demand, with a shortage of 150 units when compared to the equilibrium without intervention.
Step-by-step explanation:
When analyzing the effects of a government-imposed price restriction such as P = $40 in a perfectly competitive market with the given demand and supply functions (P = 80 - 0.2Q and P = 20 + 0.4Q), it’s important to first determine the equilibrium price and quantity without intervention. In equilibrium, the quantity demanded would be equal to the quantity supplied. To find the equilibrium, set the demand and supply functions equal to each other:
80 - 0.2Q = 20 + 0.4Q
60 = 0.6Q
Q = 100
Plugging Q back into either equation to solve for P gives us:
P = 20 + (0.4 * 100)
P = 20 + 40
P = $60
Here we see the equilibrium price is $60, and at equilibrium, the quantity is 100 units. When a price ceiling of $40 is imposed, it’s below the equilibrium price, leading to excess demand, as the quantity demanded at this price would be higher than the quantity supplied. To calculate the new quantities:
Quantity demanded at P = $40:
80 - 0.2Q = 40
0.2Q = 40
Q = 200Quantity supplied at P = $40:
20 + 0.4Q = 40
0.4Q = 20
Q = 50
The result is a shortage of 150 units, meaning quantity demanded exceeds quantity supplied by 150 units when rounded to the nearest unit.