Question

Suppose the demand and supply of manga are modeled by the two following functions:

P=60Q+59
P=−4Q+227​
Suppose the price of a manga is $18. At this price, calculate the amount of the surplus (excess supply) or shortage (excess demand); to represent an excess supply, type your answer as a positive number, and to represent an excess demand, type your answer as a negative number. If this is the equilibrium price, then instead input a value of 0 . Round your answer to two places efter the decimal point (0.01).

Answer 1

The surplus or shortage when the price is $18 can be determined by substituting the price into the demand and supply functions and solving for the quantity. In this case, there is a surplus of 62.10.

Step-by-step explanation:

Given the demand and supply functions:

P = 60Q + 59
P = -4Q + 227

We need to determine the surplus or shortage at a price of $18. To do this, we substitute P = 18 into both equations and solve for Q:

For demand: 18 = 60Q + 59
For supply: 18 = -4Q + 227

After solving, we find that the quantity demanded is 0.15 and the quantity supplied is 62.25. Therefore, there is a surplus of 62.25 - 0.15 = 62.10.