Questions: The following table shows Ellie's utility from consuming slices of pie and cans of Dr. Pepper. Slices of Pie Marginal Utility from Last Slice Cans of Dr. Pepper Marginal Utility from Last Can --- --- --- --- 0 - 0 - 1 120 1 120 2 100 2 60 3 80 3 45 4 60 4 30 5 40 5 20 6 20 6 15 Suppose Ellie has 6 per week to spend on pie and Dr. Pepper and that the price of a slice of pie is 1.00. 1.) Use the point drawing tool to plot Ellie's demand for Dr. Pepper at a price of 2.00. Label this point 'A': 2.) Use the point drawing tool to plot Ellie's demand for Dr. Pepper at a price of 0.50. Label this point 'B'. 3.) Use the line drawing tool to connect the dots to form Ellie's demand curve. Properly label this line. Carefully follow the instructions above, and only draw the required objects.

The following table shows Ellie's utility from consuming slices of pie and cans of Dr. Pepper.

Slices of Pie  Marginal Utility from Last Slice  Cans of Dr. Pepper  Marginal Utility from Last Can
---  ---  ---  ---
0  -  0  -
1  120  1  120
2  100  2  60
3  80  3  45
4  60  4  30
5  40  5  20
6  20  6  15

Suppose Ellie has 6 per week to spend on pie and Dr. Pepper and that the price of a slice of pie is 1.00.
1.) Use the point drawing tool to plot Ellie's demand for Dr. Pepper at a price of 2.00. Label this point 'A':
2.) Use the point drawing tool to plot Ellie's demand for Dr. Pepper at a price of 0.50. Label this point 'B'.
3.) Use the line drawing tool to connect the dots to form Ellie's demand curve. Properly label this line.

Carefully follow the instructions above, and only draw the required objects.
Transcript text: The following table shows Ellie's utility from consuming slices of pie and cans of Dr. Pepper. \begin{tabular}{cccc} \hline \begin{tabular}{c} Slices \\ of \\ Pie \end{tabular} & \begin{tabular}{c} Marginal Utility \\ from Last Slice \end{tabular} & \begin{tabular}{c} Cans \\ of \\ Dr. Pepper \end{tabular} & \begin{tabular}{c} Marginal \\ Utility from \\ Last Can \end{tabular} \\ \hline 0 & - & 0 & - \\ 1 & 120 & 1 & 120 \\ 2 & 100 & 2 & 60 \\ 3 & 80 & 3 & 45 \\ 4 & 60 & 4 & 30 \\ 5 & 40 & 5 & 20 \\ 6 & 20 & 6 & 15 \\ \hline \end{tabular} Suppose Ellie has $\$ 6$ per week to spend on pie and Dr. Pepper and that the price of a slice of pie is $\$ 1.00$. 1.) Use the point drawing tool to plot Ellie's demand for Dr. Pepper at a price of $\$ 2.00$. Label this point 'A': 2.) Use the point drawing tool to plot Ellie's demand for Dr. Pepper at a price of $\$ 0.50$. Label this point 'B'. 3.) Use the line drawing tool to connect the dots to form Ellie's demand curve. Properly label this line. Carefully follow the instructions above, and only draw the required objects.
failed

Solution

failed
failed

Solution Steps

Step 1: Determine Ellie's demand for Dr. Pepper at a price of $2.00

Given that the price of a slice of pie is $1.00 and the price of a can of Dr. Pepper is $2.00, we need to maximize Ellie's utility given her budget of $6.00.

  • The marginal utility per dollar for each slice of pie:

    • 1st slice: \( \frac{120}{1} = 120 \)
    • 2nd slice: \( \frac{100}{1} = 100 \)
    • 3rd slice: \( \frac{80}{1} = 80 \)
    • 4th slice: \( \frac{60}{1} = 60 \)
    • 5th slice: \( \frac{40}{1} = 40 \)
    • 6th slice: \( \frac{20}{1} = 20 \)
  • The marginal utility per dollar for each can of Dr. Pepper:

    • 1st can: \( \frac{120}{2} = 60 \)
    • 2nd can: \( \frac{60}{2} = 30 \)
    • 3rd can: \( \frac{45}{2} = 22.5 \)
    • 4th can: \( \frac{30}{2} = 15 \)
    • 5th can: \( \frac{20}{2} = 10 \)
    • 6th can: \( \frac{15}{2} = 7.5 \)

To maximize utility, Ellie should spend her money on the items with the highest marginal utility per dollar first.

  • 1st slice of pie: 120
  • 2nd slice of pie: 100
  • 3rd slice of pie: 80
  • 4th slice of pie: 60
  • 1st can of Dr. Pepper: 60
  • 5th slice of pie: 40

Ellie will buy 4 slices of pie and 1 can of Dr. Pepper, spending $4 on pie and $2 on Dr. Pepper.

Step 2: Determine Ellie's demand for Dr. Pepper at a price of $0.50

Given that the price of a slice of pie is $1.00 and the price of a can of Dr. Pepper is $0.50, we need to maximize Ellie's utility given her budget of $6.00.

  • The marginal utility per dollar for each can of Dr. Pepper:
    • 1st can: \( \frac{120}{0.5} = 240 \)
    • 2nd can: \( \frac{60}{0.5} = 120 \)
    • 3rd can: \( \frac{45}{0.5} = 90 \)
    • 4th can: \( \frac{30}{0.5} = 60 \)
    • 5th can: \( \frac{20}{0.5} = 40 \)
    • 6th can: \( \frac{15}{0.5} = 30 \)

To maximize utility, Ellie should spend her money on the items with the highest marginal utility per dollar first.

  • 1st can of Dr. Pepper: 240
  • 2nd can of Dr. Pepper: 120
  • 3rd can of Dr. Pepper: 90
  • 4th can of Dr. Pepper: 60
  • 1st slice of pie: 120
  • 5th can of Dr. Pepper: 40

Ellie will buy 4 cans of Dr. Pepper and 1 slice of pie, spending $2 on pie and $2 on Dr. Pepper.

Step 3: Plot the points and draw the demand curve
  • Point A: (2.00, 1)
  • Point B: (0.50, 4)

Final Answer

Ellie's demand for Dr. Pepper at different prices is as follows:

  • At $2.00 per can, she demands 1 can.
  • At $0.50 per can, she demands 4 cans.

{"axisType": 3, "coordSystem": {"xmin": 0, "xmax": 3, "ymin": 0, "ymax": 5}, "commands": ["y = 1", "y = 4"], "latex_expressions": ["$A: (2.00, 1)$", "$B: (0.50, 4)$"]}

Was this solution helpful?
failed
Unhelpful
failed
Helpful