Question

Suppose the market supply of a good is given by P = 10 + 0.2Q, the market demand is given by P = 60 - 0.5Q, and the market is in equilibrium. If the government imposes a price restriction of P = $20 per unit, then subsequent to this market intervention there will be a:

1) Surplus of the good
2) Shortage of the good
3) No change in the quantity of the good
4) Decrease in the quantity of the good

Answer 1

Imposing a price restriction of P = $20 in a market where the supply is P = 10 + 0.2Q and the demand is P = 60 - 0.5Q, creates a shortage because the quantity demanded at this price is greater than the quantity supplied.

Step-by-step explanation:

When analyzing the market for a good where the market supply is given by P = 10 + 0.2Q, and the market demand is given by P = 60 - 0.5Q, finding the equilibrium situation means setting the two equations equal to each other since at equilibrium, supply equals demand. In such a case, the equilibrium price (Pe) and equilibrium quantity (Qe) can be found. However, if the government imposes a price restriction such as P = $20, this changes the conditions of the market.

With a price set at $20, the quantity demanded (based on the demand equation P = 60 - 0.5Q) becomes higher than the quantity supplied (based on the supply equation P = 10 + 0.2Q). Consequently, this creates a situation where the quantity demanded exceeds the quantity supplied, which is known as a shortage. If instead, the government set a price above the equilibrium price, this would lead to a surplus, where the quantity supplied would exceed the quantity demanded.