Let's break down the problem step by step.
1. Identifying the Minimum Acceptable Price:
- The minimum acceptable price is the lowest price that producer Sam is willing to accept for his product. In this case, this minimum acceptable price is [tex]\( \$15 \)[/tex].
2. Identifying the Market Price:
- The market price is the price Sam could actually get for the product in the market. Here, the market price is [tex]\( \$78 \)[/tex].
3. Understanding Producer Surplus:
- Producer surplus is the difference between the market price and the minimum acceptable price. It represents the benefit or additional profit that the producer receives from selling at the market price rather than the minimum acceptable price.
4. Calculating the Producer Surplus:
- The formula for producer surplus is:
[tex]\[
\text{Producer Surplus} = \text{Market Price} - \text{Minimum Acceptable Price}
\][/tex]
- Substituting in the given values:
[tex]\[
\text{Producer Surplus} = 78 - 15
\][/tex]
- Performing the subtraction:
[tex]\[
\text{Producer Surplus} = 63
\][/tex]
Therefore, Sam's producer surplus is [tex]\( \$63 \)[/tex]. This means that Sam gains an additional [tex]\( \$63 \)[/tex] by being able to sell his product at the market price of [tex]\( \$78 \)[/tex], compared to his minimum acceptable price of [tex]\( \$15 \)[/tex].
