Question

Assume that the market demand function is: Q(D) = 2000 - 5P And the market supply function is: Q(S) = 100 + 5P Assume that the government passes legislation that sets the maximum price to $100 a unit. Which of the following statements are correct (multiple statements may be correct)?

1.) At a legally mandated price of $100 a unit, quantity demanded is equal to 1050 and quantity supplied is equal to 1050, therefore the legally mandated price has no impact on the market.

2.) At a legally mandated price of $100 a unit, quantity demanded is equal to 1500 and the quantity supplied is equal to 600, therefore the shortage is equal to 900 units.

3.) At a legally mandated price of $100 a unit, quantity demanded is equal to 600 while quantity supplied is equal to 1500, therefore there is a surplus in the market of 900 units, not a shortage.

4.) At a legally mandated price of $100 a unit, quantity demanded rises from 1050 units to 1500 units and quantity supplied falls from 1050 units to 600 units, resulting in a shortage of 900 units.

Answer 1

Answer : The answer is option 4.

Before government imposed legally mandated price :

Demand :  Q = 2000 - 5P

=> 5P = 2000 - Q

=> P = (2000 - Q) / 5

=> P = 400 - 0.2Q

Supply : Q = 100 + 5P

=> Q - 100 = 5P

=> P = (Q - 100) / 5

=> P = 0.2Q - 20

At equilibrium demand = supply.

=> 400 - 0.2Q = 0.2Q - 20

=> 400 + 20 = 0.2Q + 0.2Q

=> 420 = 0.4Q

=> Q = 420 / 0.4

=> Q = 1050

Therefore, before imposing legally mandated price $100 per unit, the quantity demanded and quantity supplied is 1050 units.

After imposing legally mandated price :

Demand : Q = 2000 - (5 * 100)

=> Q = 1500 units.

Supply : Q = 100 + (5 * 100)

=> Q = 600 units.

Shortage = Quantity demanded - Quantity supplied = 1500 - 600 = 900 units

Therefore, at legally mandated price $100 per unit the quantity demanded increases from 1050 units to 1500 units and quantity supplied decreases from 1050 units to 600 units. As a result, there occurs a shortage of 900 units.

So, option 4 is correct.