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.

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To solve the problem, we will follow the steps outlined: ### Part (a): Find the equilibrium price and quantity 1. **Equilibrium Condition**: The equilibrium price occurs when quantity supplied $$ S(p) $$ equals quantity demanded $$ D(p) $$. Therefore, we set the two equations equal to each other: $$ S(p) = D(p) $$ Substituting the given functions: $$ -340 + 40p = 1100 - 50p $$ 2. **Solving for $$ p $$**: - Rearranging the equation: $$ 40p + 50p = 1100 + 340 $$ $$ 90p = 1440 $$ $$ p = \frac{1440}{90} = 16 $$ 3. **Finding the Equilibrium Quantity**: Now that we have the equilibrium price $$ p = 16 $$, we can substitute this back into either the supply or demand function to find the equilibrium quantity: $$ S(16) = -340 + 40(16) = -340 + 640 = 300 $$ Thus, the equilibrium quantity is 300 T-shirts. ### Part (b): Determine the prices for which quantity demanded is greater than quantity supplied 1. **Setting up the inequality**: We need to find the price $$ p $$ for which $$ D(p) > S(p) $$: $$ 1100 - 50p > -340 + 40p $$ 2. **Solving the inequality**: - Rearranging the inequality: $$ 1100 + 340 > 50p + 40p $$ $$ 1440 > 90p $$ $$ p < \frac{1440}{90} = 16 $$ ### Conclusion for Part (b): The prices for which quantity demanded is greater than quantity supplied are: $$ p < 16 $$ Thus, the answer is: For the price $$ \$ $$ $$ \square $$ $$ 16 $$ the quantity demanded is greater than quantity supplied. ### Summary of Answers: - (a) Equilibrium price: $$ \$ 16 $$, Equilibrium quantity: $$ 300 $$ T-shirts. - (b) For the price $$ \$ $$ $$ 16 $$ the quantity demanded is greater than quantity supplied. - **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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