Calculate the Equilibrium Price for College Newspapers

Question:

The demand and supply functions for your college newspaper are, q = −11,000p + 6,900 and q = 5,000p + 500, respectively, where p is the price in dollars. At what price should the newspapers be sold so that there is neither a surplus nor a shortage of papers?

To solve this problem, we need to find the price at which the demand for the college newspaper equals the supply, ensuring there is neither a surplus nor a shortage.

Given:

• Demand function: qd=−11,000p+6,900q_d = -11,000p + 6,900qd​=−11,000p+6,900
• Supply function: qs=5,000p+500q_s = 5,000p + 500qs​=5,000p+500

Here, $p$ represents the price of the newspaper in dollars, and $q$ represents the quantity demanded or supplied.

Solution:

To find the equilibrium price where demand equals supply, set the two equations equal to each other:

$$-11,000p+6,900=5,000p+500$$

Step-by-step Solution:

1. Combine like terms:

   $$6,900-500=5,000p+11,000p$$ $$6,400=16,000p$$

2. Solve for $p$:

   p=6,40016,000p = \frac{6,400}{16,000}p=16,0006,400​ $$p=0.4$$

At Last:

The newspapers should be sold for $0.40 to ensure there is neither a surplus nor a shortage.

This equilibrium price balances the demand and supply, ensuring that the quantity demanded by students matches the quantity the college can supply