9. (LO4) Find the producer's surplus at Q=5 for the supply function P=23+2Q a). 5 b). 10 c). 15 d). 20 e). 25

To find the producer's surplus at \( Q = 5 \) for the supply function \( P = 23 + 2Q \), we need to follow these steps:<br /><br />1. **Determine the market price at \( Q = 5 \)**:<br /> \[<br /> P = 23 + 2(5) = 23 + 10 = 33<br /> \]<br /><br />2. **Find the supply function's intercept (i.e., the price when \( Q = 0 \))**:<br /> \[<br /> P = 23 + 2(0) = 23<br /> \]<br /><br />3. **Calculate the area of the triangle formed by the supply curve, the price level at \( Q = 5 \), and the price level at \( Q = 0 \)**:<br /> The base of the triangle is the difference in price levels, and the height is the quantity \( Q = 5 \).<br /><br /> \[<br /> \text{Base} = 33 - 23 = 10<br /> \]<br /> \[<br /> \text{Height} = 5<br /> \]<br /><br />4. **Calculate the area of the triangle**:<br /> \[<br /> \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 10 \times 5 = 25<br /> \]<br /><br />Therefore, the producer's surplus at \( Q = 5 \) is \( 25 \).<br /><br />The correct answer is:<br />e). 25