The demand for your college newspaper is 6,000 copies each week if the paper is given away free of charge, and drops to 5,000 each week if the charge is 10¢ per copy. However, the university is prepared to supply only 300 copies per week free of charge, but will supply 2,100 each week at 20¢ per copy.
(a)
Write down the associated linear demand and supply functions. (p is in dollars.)
demand function	q(p)	=	
  
Incorrect: Your answer is incorrect.
supply function	q(p)	=	
  
Incorrect: Your answer is incorrect.
(b)
At what price (in dollars) should the college newspapers be sold so that there is neither a surplus nor a shortage of college newspapers?
$ 

We are asked to find the demand and supply functions for a college newspaper and determine the price at which there is neither a surplus nor a shortage (i.e., equilibrium price).

### (a) Demand and Supply Functions

#### Demand Function:
We are given two demand points:
- When the price is $0 (free), the demand is 6,000 copies.
- When the price is $0.10 (10¢), the demand drops to 5,000 copies.

Using these points $(p, q)$, we can find the equation of the demand line. The general form of the demand function is:
\[
q(p) = m_d p + b_d
\]
where $q(p)$ is the quantity demanded, $p$ is the price in dollars, $m_d$ is the slope of the demand function, and $b_d$ is the intercept.

We can first calculate the slope $m_d$ using the formula for the slope of a line between two points $(p_1, q_1)$ and $(p_2, q_2)$:
\[
m_d = \frac{q_2 - q_1}{p_2 - p_1} = \frac{5000 - 6000}{0.10 - 0} = \frac{-1000}{0.10} = -10,000
\]
So, the slope $m_d = -10,000$.

Now, using the point $(p = 0, q = 6000)$, we can find the intercept $b_d$:
\[
q(0) = -10,000(0) + b_d = 6000 \implies b_d = 6000
\]

Thus, the demand function is:
\[
q(p) = -10,000 p + 6000
\]

#### Supply Function:
We are given two supply points:
- When the price is $0 (free), the supply is 300 copies.
- When the price is $0.20 (20¢), the supply is 2,100 copies.

Using these points $(p, q)$, we find the equation of the supply line. The general form of the supply function is:
\[
q(p) = m_s p + b_s
\]
where $q(p)$ is the quantity supplied, $m_s$ is the slope of the supply function, and $b_s$ is the intercept.

We calculate the slope $m_s$ using the points $(0, 300)$ and $(0.20, 2100)$:
\[
m_s = \frac{2100 - 300}{0.20 - 0} = \frac{1800}{0.20} = 9000
\]
So, the slope $m_s = 9000$.

Now, using the point $(p = 0, q = 300)$, we find the intercept $b_s$:
\[
q(0) = 9000(0) + b_s = 300 \implies b_s = 300
\]

Thus, the supply function is:
\[
q(p) = 9000 p + 300
\]

### (b) Finding the Equilibrium Price:
At the equilibrium point, the quantity demanded equals the quantity supplied, i.e., $q_{\text{demand}}(p) = q_{\text{supply}}(p)$. We set the two equations equal to each other:
\[
-10,000 p + 6000 = 9000 p + 300
\]

Now solve for $p$:
\[
6000 - 300 = 9000 p + 10,000 p
\]
\[
5700 = 19,000 p
\]
\[
p = \frac{5700}{19,000} = 0.30
\]

Thus, the equilibrium price is **$0.30** (30¢).

### Summary:
- The demand function is: $q(p) = -10,000 p + 6000$
- The supply function is: $q(p) = 9000 p + 300$
- The equilibrium price is: **$0.30**

Do you have any questions or want further details?

Here are 5 related questions:
1. What would happen to the demand if the price increases to $0.50?
2. How would the equilibrium price change if the supply increased to 3,000 copies at $0.20?
3. How do shifts in demand or supply curves affect the equilibrium price and quantity?
4. What is the significance of a surplus or shortage in economic markets?
5. How do we interpret the slope of demand and supply functions in real-world situations?

**Tip:** The steeper the slope of a demand curve, the more sensitive demand is to price changes.

The demand for your college newspaper is 6,000 copies each week if the paper is given away free of charge, and drops to 5,000 each week if the charge is 10¢ per copy. However, the university is prepared to supply only 300 copies per week free of charge, but will supply 2,100 each week at 20¢ per copy.
(a) Write down the associated linear demand and supply functions. (p is in dollars.)
(b) At what price (in dollars) should the college newspapers be sold so that there is neither a surplus nor a shortage of college newspapers?

Learn how to find the linear demand and supply functions for a college newspaper with given data points, and how to calculate the equilibrium price where supply meets demand. This problem covers key economic and algebraic concepts, ideal for high school students in Grades 11-12.

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