If both members and non-members are allowed to purchase tickets to this year's celebrity golf tournament and the country club sets the ticket price at [tex]$20, what will be the result?

| Price | Members | Non-members | Total |
|-------|---------|-------------|-------|
| $[/tex]10 | 1000 | 500 | 1500 |
| [tex]$15 | 800 | 400 | 1200 |
| $[/tex]20 | 600 | 300 | 900 |
| [tex]$25 | 400 | 200 | 600 |
| $[/tex]30 | 200 | 100 | 300 |

A. A shortage of 300 tickets.
B. A surplus of 300 tickets.
C. 30 tickets sold.
D. 600 tickets unsold.



Answer :

Let's break this down step-by-step.

We are given a table that shows the number of tickets demanded by members and non-members at different price points alongside a constant quantity supplied at each price point.

We need to focus on the scenario where the ticket price is set at [tex]$20. From the table, we can extract the relevant data: - At $[/tex]\[tex]$20$[/tex], the number of tickets demanded by members is 600.
- At [tex]$\$[/tex]20[tex]$, the number of tickets demanded by non-members is 300. - The quantity supplied at $[/tex]\[tex]$20$[/tex] is 600 tickets.

Now, let's calculate the total demand at this price point:

[tex]\[ \text{Total demand} = \text{Demand by members} + \text{Demand by non-members} \][/tex]

Substituting the given values:

[tex]\[ \text{Total demand} = 600 + 300 = 900 \text{ tickets} \][/tex]

Next, we compare the total demand to the quantity supplied to determine if there is a shortage or surplus:

[tex]\[ \text{Quantity supplied} = 600 \text{ tickets} \][/tex]

We subtract the quantity supplied from the total demand to find the difference:

[tex]\[ \text{Difference} = \text{Quantity supplied} - \text{Total demand} = 600 - 900 = -300 \text{ tickets} \][/tex]

Since the result is negative, it means there is a shortage, as the demand exceeds the supply. Specifically, there is a shortage of 300 tickets.

Thus, the correct answer is:

a shortage of 300 tickets.