Consider a market where the demand and supply for the good are described by the following equations: begin mathsize 14px style straight Q subscript straight D space equals space 225 space minus space 3 straight P end style and begin mathsize 14px style straight Q subscript straight S space equals space minus space 22.5 space plus space 1.5 straight P end style.

If the government implements a price ceiling of $45, this will result in a

A. surplus of 22.5 units.

B. a surplus of 45 units.

C. a shortage of 45 units.

D. a shortage of 22.5 units.

Question

Business

Houston Valdez

29 May, 01:41

Consider a market where the demand and supply for the good are described by the following equations: begin mathsize 14px style straight Q subscript straight D space equals space 225 space minus space 3 straight P end style and begin mathsize 14px style straight Q subscript straight S space equals space minus space 22.5 space plus space 1.5 straight P end style.

If the government implements a price ceiling of $45, this will result in a

A. surplus of 22.5 units.

B. a surplus of 45 units.

C. a shortage of 45 units.

D. a shortage of 22.5 units.

+4

Answers (1)

Know the Answer?

Jamie Knight · Answer 1

The correct option is (c) a shortage of 45 units.

Explanation:

Solution

Given that:

Qd=225-3P

Qs=-22.5+1.5P

Then,

Set Qd=Qs for equilibrium

225-3P=-22.5+1.5P

4.5P=247.50

P=$55

Now

The government forces a ceiling of $45, it is binding as it is lesser than the equilibrium price.

Thus,

Let calculate the demanded quantity and supplied quantity at a price of $45

Now,

Qd=225-3*45=90

Qs=-22.5+1.5*45=45

Shortage=Qd-Qs=90-45=45 units.

Therefore, there is a shortage of 45 units.