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Part 3 of 4 Points: 0 of 1 Suppose that the quantity supplied \( S \) and quantity demanded \( D \) of T-shirts at a concert are given by the following functions where \( p \) is the price. \[ \begin{array}{l} S(p)=-340+40 p \\ D(p)=1100-50 p \end{array} \] Arrswer parts (a) through (c). (a) Find the equilibrium price for the \( T \)-shirts at this concert The equilibrium price is \( \$ 16 \) (Round to the nearest dollar as needed.) What is the equilibrium quantity? The equilibrium quantity is 300 T -shirts. (Type a whole number.) (b) Determine the prices for which quantity demanded is greater than quantity supplied. For the orice \( \$ \) \( \square \) \( \square \) \( \square \) \( \$ \square \) the quantity demanded is greater than quantity supplied.

Ask by Ross Mcguire. in the United States
Mar 13,2025

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- **Part (a):** - **Equilibrium Price:** \$16 - **Equilibrium Quantity:** 300 T-shirts - **Part (b):** - Quantity demanded is greater than quantity supplied when the price is less than \$16.

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To find the range of prices for which the quantity demanded is greater than the quantity supplied, we can set the quantity demanded \( D(p) \) greater than the quantity supplied \( S(p) \): \[ 1100 - 50p > -340 + 40p \] Now, let's simplify this inequality: \[ 1100 + 340 > 50p + 40p \] \[ 1440 > 90p \] Dividing both sides by 90 gives: \[ p < \frac{1440}{90} \approx 16 \] So, the price range at which the quantity demanded exceeds the quantity supplied is: For the price \( \$ \) **less than 16**, the quantity demanded is greater than quantity supplied.

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