Chapter 3.1, Problem 39AYU

(a)

To determine

To calculate: The quantity of the equilibrium price for T-shirts at this concert.

Answer to Problem 39AYU

The equilibrium quantity is $16$ .

Explanation of Solution

Given information:

The quantity supplied $S$ and quantity demanded $D$ of T-shirts at a concert are given by the following functions.

  $\begin{array}{l}S\left(p\right)=-200+50p\\ D\left(p\right)=1000-25p\end{array}$

Where $p$ = price of t-shirt.

Formula used:

  $\begin{array}{l}S\left(p\right)=-200+50p\\ D\left(p\right)=1000-25p\end{array}$

Calculation:

Quantity of the equilibrium price for T-shirts at this concert is calculated as:

  $\begin{array}{l}S\left(p\right)=-200+50p\\ D\left(p\right)=1000-25p\\ S\left(p\right)=D\left(p\right)\\ -200+50p=1000-25p\\ 75p=1200\\ p=16\end{array}$

b.

To determine

To calculated:

The prices for which quantity demanded is greater than quantity supplied.

Answer to Problem 39AYU

The prices for which quantity demanded is greater than quantity supplied is $16$ .

Explanation of Solution

Given information:

  $\begin{array}{l}S\left(p\right)=-200+50p\\ D\left(p\right)=1000-25p\end{array}$

Where $p$ = price of t-shirt.

Formula used:

  $\begin{array}{l}S\left(p\right)=-200+50p\\ D\left(p\right)=1000-25p\end{array}$

Calculation:

Prices for which quantity demanded is greater than quantity supplied is calculated as:

  $\begin{array}{l}-200+50p<1000-25p\\ 75p<1200\\ p<16\end{array}$

c.

To determine

To calculate: thing which will eventually happen to the price of t shirts if quantity demanded is greater than quality supplied.

Answer to Problem 39AYU

The statement is explained.

Explanation of Solution

Given information:

  $\begin{array}{l}S\left(p\right)=-200+50p\\ D\left(p\right)=1000-25p\end{array}$

Where $p$ = price of t-shirt.

Formula used:

  $\begin{array}{l}S\left(p\right)=-200+50p\\ D\left(p\right)=1000-25p\end{array}$

  $S\left(p\right)>D\left(p\right)$

If the quantity demanded is less than quantity supplied then the prices of t-shirts will decrease.