Chapter 1, Problem 13P

a.

To determine

Make a table of the student who says “yes” at each price level.

Answer to Problem 13P

The table is,

  

Explanation of Solution

Given: The price table,

  $\begin{array}{cc}Price& Yes or No\\ 30¢& \\ 40¢& \\ 50¢& \\ 60¢& \\ 70¢& \\ 80¢& \\ 90¢& \\ \$1.0& \\ \$1.1& \\ \$1.2& \end{array}$

Calculation:

The function “RANDBETWEEN(1,40)” is used in the excel to make a table.

Let’s take there are 200 students in the class. During the survey 39 students say “yes” to pay $30¢$ , 17 students say “yes” to pay $40¢$ , 32 students say “yes” to pay $50¢$ , 12 students say “yes” to pay $60¢$ , 39 students say “yes” to pay $70¢$ , 5 students say “yes” to pay $80¢$ , 1 students say “yes” to pay $90¢$ , 35 students say “yes” to pay $\$1.0$ , 19 students say “yes” to pay $\$1.1$ , and 1 students say “yes” to pay $\$1.2$ for a candy bar.

b.

To determine

Sketch a scatter plot for a data which is found in part (a).

Answer to Problem 13P

The graph is,

  

Explanation of Solution

Given: The data which is found in part (a),

  $\begin{array}{cc}Price& Yes\\ 30¢& 36\\ 40¢& 10\\ 50¢& 6\\ 60¢& 10\\ 70¢& 15\\ 80¢& 12\\ 90¢& 38\\ \$1.0& 3\\ \$1.1& 24\\ \$1.2& 7\end{array}$

Calculation:

Using Excel to scetch a scatter plot.

• Write the data in the excel and plot using chart “scatter”.

c.

To determine

Draw a regression line.

Answer to Problem 13P

The solution is,

  

Explanation of Solution

Given: The data set is,

  $\begin{array}{cc}Price& Yes\\ 30¢& 36\\ 40¢& 10\\ 50¢& 6\\ 60¢& 10\\ 70¢& 15\\ 80¢& 12\\ 90¢& 38\\ \$1.0& 3\\ \$1.1& 24\\ \$1.2& 7\end{array}$

Calculation:

The regression line is defined as,

  $y\text{'}=a+bt \mathrm{.....}(1)$

Find the value of a and b using relation,

  $\begin{array}{l}a=\frac{\left({\displaystyle \sum y}\right)\left({\displaystyle \sum x^2}\right)-\left({\displaystyle \sum x}\right)\left({\displaystyle \sum xy}\right)}{n\left({\displaystyle \sum x^2}\right)-{\left({\displaystyle \sum x}\right)}^2}\\ b=\frac{n\left({\displaystyle \sum xy}\right)-\left({\displaystyle \sum x}\right)\left({\displaystyle \sum y}\right)}{n\left({\displaystyle \sum x^2}\right)-{\left({\displaystyle \sum x}\right)}^2}\end{array}$

After simplifying the value of a and b, put into the equation (1) and get the solution.

Using Excel to scetch a scatter plot.

d.

To determine

Explain what is p-intercept of the demand equation.

Answer to Problem 13P

The price-intercept is defined as the price at which quantity demand equals to zero.

Explanation of Solution

Given: The data set is,

  $\begin{array}{cc}Price& Yes\\ 30¢& 36\\ 40¢& 10\\ 50¢& 6\\ 60¢& 10\\ 70¢& 15\\ 80¢& 12\\ 90¢& 38\\ \$1.0& 3\\ \$1.1& 24\\ \$1.2& 7\end{array}$

Calculation:

The quantity demand equation is defined as,

  $Qd=a-bP$

Where, $Qd$ is the quantity demand, $a$ is the maximum value, $b$ is the slope of the data set. P is the price-intercept.

Let’s take $Qd=0$ to calculate price-intercept then,

  $\begin{array}{l}0=38-(-12.1212)P\\ P=\frac{38-0}{12.1212}\\ P=3.135\$\end{array}$