The figure below represents the weekly demand for GPS units. Instructions: Round your answers to two decimal places. If you are entering a negative number include a minus sign. a. Using the starting point formula,  what is the price elasticity of demand for going from a price of $160 per unit to a price of $140 per unit?         b. Using the starting point formula,  what is the price elasticity of demand for going from a price of $140 per unit to a price of $160 per unit?         c. Using the midpoint formula, what is the midpoint price elasticity of demand for GPS units between a price of $140 per unit and a price of $160 per unit?        d. Using the starting point formula, what is the price elasticity of demand for going from a price of $40 per unit to a price of $20 per unit?           e. Using the starting point formula,  what is the price elasticity of demand for going from a price of $20 per unit to a price of $40 per unit?         f. Using the midpoint formula, what is the midpoint price elasticity of demand for GPS units between a price of $20 per unit and a price of $40 per unit?

To answer the questions step by step, we need to use the formulas for price elasticity of demand. The starting point formula and the midpoint formula are used to calculate the elasticity.

a. Using the starting point formula, what is the price elasticity of demand for going from a price of $160 per unit to a price of$140 per unit?

1. Starting Point Formula: $E_d = \frac{\Delta Q / Q_1}{\Delta P / P_1}$ where $\Delta Q$ is the change in quantity demanded, $Q_1$ is the initial quantity demanded, $\Delta P$ is the change in price, and $P_1$ is the initial price.

2. Given:

   • Initial price $P_1 = \$160$
   • New price $P_2 = \$140$
   • Initial quantity demanded $Q_1$ and new quantity demanded $Q_2$ need to be determined from the figure.

3. Calculate:

   • Change in price $\Delta P = P_2 - P_1 = 140 - 160 = -20$
   • Change in quantity demanded $\Delta Q = Q_2 - Q_1$

4. Substitute: $E_d = \frac{\Delta Q / Q_1}{-20 / 160}$

5. Solve:

   • Find $Q_1$ and $Q_2$ from the figure.
   • Calculate $\Delta Q$.
   • Substitute values into the formula to find $E_d$.

b. Using the starting point formula, what is the price elasticity of demand for going from a price of $140 per unit to a price of$160 per unit?

1. Given:

   • Initial price $P_1 = \$140$
   • New price $P_2 = \$160$
   • Initial quantity demanded $Q_1$ and new quantity demanded $Q_2$ need to be determined from the figure.

2. Calculate:

   • Change in price $\Delta P = P_2 - P_1 = 160 - 140 = 20$
   • Change in quantity demanded $\Delta Q = Q_2 - Q_1$

3. Substitute: $E_d = \frac{\Delta Q / Q_1}{20 / 140}$

4. Solve:

   • Find $Q_1$ and $Q_2$ from the figure.
   • Calculate $\Delta Q$.
   • Substitute values into the formula to find $E_d$.

c. Using the midpoint formula, what is the midpoint price elasticity of demand for GPS units between a price of $140 per unit and a price of$160 per unit?

1. Midpoint Formula: $E_d = \frac{\Delta Q / \left(\frac{Q_1 + Q_2}{2}\right)}{\Delta P / \left(\frac{P_1 + P_2}{2}\right)}$

2. Given:

   • Prices $P_1 = \$140$ and $P_2 = \$160$
   • Quantities $Q_1$ and $Q_2$ need to be determined from the figure.

3. Calculate:

   • Change in price $\Delta P = P_2 - P_1 = 20$
   • Change in quantity demanded $\Delta Q = Q_2 - Q_1$
   • Average price $\frac{P_1 + P_2}{2} = \frac{140 + 160}{2} = 150$
   • Average quantity $\frac{Q_1 + Q_2}{2}$

4. Substitute: $E_d = \frac{\Delta Q / \left(\frac{Q_1 + Q_2}{2}\right)}{20 / 150}$

5. Solve:

   • Find $Q_1$ and $Q_2$ from the figure.
   • Calculate $\Delta Q$.
   • Substitute values into the formula to find $E_d$.

d. Using the starting point formula, what is the price elasticity of demand for going from a price of $40 per unit to a price of$20 per unit?

1. Given:

   • Initial price $P_1 = \$40$
   • New price $P_2 = \$20$
   • Initial quantity demanded $Q_1$ and new quantity demanded $Q_2$ need to be determined from the figure.

2. Calculate:

   • Change in price $\Delta P = P_2 - P_1 = 20 - 40 = -20$
   • Change in quantity demanded $\Delta Q = Q_2 - Q_1$

3. Substitute: $E_d = \frac{\Delta Q / Q_1}{-20 / 40}$

4. Solve:

   • Find $Q_1$ and $Q_2$ from the figure.
   • Calculate $\Delta Q$.
   • Substitute values into the formula to find $E_d$.

e. Using the starting point formula, what is the price elasticity of demand for going from a price of $20 per unit to a price of$40 per unit?

1. Given:

   • Initial price $P_1 = \$20$
   • New price $P_2 = \$40$
   • Initial quantity demanded $Q_1$ and new quantity demanded $Q_2$ need to be determined from the figure.

2. Calculate:

   • Change in price $\Delta P = P_2 - P_1 = 40 - 20 = 20$
   • Change in quantity demanded $\Delta Q = Q_2 - Q_1$

3. Substitute: $E_d = \frac{\Delta Q / Q_1}{20 / 20}$

4. Solve:

   • Find $Q_1$ and $Q_2$ from the figure.
   • Calculate $\Delta Q$.
   • Substitute values into the formula to find $E_d$.

f. Using the midpoint formula, what is the midpoint price elasticity of demand for GPS units between a price of $20 per unit and a price of$40 per unit?

1. Midpoint Formula: $E_d = \frac{\Delta Q / \left(\frac{Q_1 + Q_2}{2}\right)}{\Delta P / \left(\frac{P_1 + P_2}{2}\right)}$

2. Given:

   • Prices $P_1 = \$20$ and $P_2 = \$40$
   • Quantities $Q_1$ and $Q_2$ need to be determined from the figure.

3. Calculate:

   • Change in price $\Delta P = P_2 - P_1 = 20$
   • Change in quantity demanded $\Delta Q = Q_2 - Q_1$
   • Average price $\frac{P_1 + P_2}{2} = \frac{20 + 40}{2} = 30$
   • Average quantity $\frac{Q_1 + Q_2}{2}$

4. Substitute: $E_d = \frac{\Delta Q / \left(\frac{Q_1 + Q_2}{2}\right)}{20 / 30}$

5. Solve:

   • Find $Q_1$ and $Q_2$ from the figure.
   • Calculate $\Delta Q$.
   • Substitute values into the formula to find $E_d$.

Note: To complete the calculations, you need the specific quantities $Q_1$ and $Q_2$ from the figure provided in the question.

To answer the questions step by step, we need to use the formulas for price elasticity of demand. The starting point formula and the midpoint formula are used to calculate the price elasticity of demand.

Starting Point Formula: $E_d = \frac{\Delta Q / Q_1}{\Delta P / P_1}$

Midpoint Formula: $E_d = \frac{\Delta Q / \left(\frac{Q_1 + Q_2}{2}\right)}{\Delta P / \left(\frac{P_1 + P_2}{2}\right)}$

Where:

• $\Delta Q$ is the change in quantity demanded.
• $Q_1$ and $Q_2$ are the initial and final quantities demanded, respectively.
• $\Delta P$ is the change in price.
• $P_1$ and $P_2$ are the initial and final prices, respectively.

Let's assume the quantities demanded at different prices are given as follows:

• At $160 per unit, the quantity demanded is 100 units.
• At $140 per unit, the quantity demanded is 150 units.
• At $40 per unit, the quantity demanded is 400 units.
• At $20 per unit, the quantity demanded is 600 units.

Now, let's solve each part step by step.

a. Using the starting point formula, what is the price elasticity of demand for going from a price of $160 per unit to a price of$140 per unit?

1. Initial price $P_1 = 160$
2. Final price $P_2 = 140$
3. Initial quantity $Q_1 = 100$
4. Final quantity $Q_2 = 150$
5. Change in price $\Delta P = P_2 - P_1 = 140 - 160 = -20$
6. Change in quantity $\Delta Q = Q_2 - Q_1 = 150 - 100 = 50$

$E_d = \frac{50 / 100}{-20 / 160} = \frac{0.5}{-0.125} = -4.00$

b. Using the starting point formula, what is the price elasticity of demand for going from a price of $140 per unit to a price of$160 per unit?

1. Initial price $P_1 = 140$
2. Final price $P_2 = 160$
3. Initial quantity $Q_1 = 150$
4. Final quantity $Q_2 = 100$
5. Change in price $\Delta P = P_2 - P_1 = 160 - 140 = 20$
6. Change in quantity $\Delta Q = Q_2 - Q_1 = 100 - 150 = -50$

$E_d = \frac{-50 / 150}{20 / 140} = \frac{-0.3333}{0.1429} = -2.33$

c. Using the midpoint formula, what is the midpoint price elasticity of demand for GPS units between a price of $140 per unit and a price of$160 per unit?

1. Initial price $P_1 = 160$
2. Final price $P_2 = 140$
3. Initial quantity $Q_1 = 100$
4. Final quantity $Q_2 = 150$
5. Change in price $\Delta P = P_2 - P_1 = 140 - 160 = -20$
6. Change in quantity $\Delta Q = Q_2 - Q_1 = 150 - 100 = 50$
7. Average price $\frac{P_1 + P_2}{2} = \frac{160 + 140}{2} = 150$
8. Average quantity $\frac{Q_1 + Q_2}{2} = \frac{100 + 150}{2} = 125$

$E_d = \frac{50 / 125}{-20 / 150} = \frac{0.4}{-0.1333} = -3.00$

d. Using the starting point formula, what is the price elasticity of demand for going from a price of $40 per unit to a price of$20 per unit?

1. Initial price $P_1 = 40$
2. Final price $P_2 = 20$
3. Initial quantity $Q_1 = 400$
4. Final quantity $Q_2 = 600$
5. Change in price $\Delta P = P_2 - P_1 = 20 - 40 = -20$
6. Change in quantity $\Delta Q = Q_2 - Q_1 = 600 - 400 = 200$

$E_d = \frac{200 / 400}{-20 / 40} = \frac{0.5}{-0.5} = -1.00$

e. Using the starting point formula, what is the price elasticity of demand for going from a price of $20 per unit to a price of$40 per unit?

1. Initial price $P_1 = 20$
2. Final price $P_2 = 40$
3. Initial quantity $Q_1 = 600$
4. Final quantity $Q_2 = 400$
5. Change in price $\Delta P = P_2 - P_1 = 40 - 20 = 20$
6. Change in quantity $\Delta Q = Q_2 - Q_1 = 400 - 600 = -200$

$E_d = \frac{-200 / 600}{20 / 20} = \frac{-0.3333}{1} = -0.33$

f. Using the midpoint formula, what is the midpoint price elasticity of demand for GPS units between a price of $20 per unit and a price of$40 per unit?

1. Initial price $P_1 = 20$
2. Final price $P_2 = 40$
3. Initial quantity $Q_1 = 600$
4. Final quantity $Q_2 = 400$
5. Change in price $\Delta P = P_2 - P_1 = 40 - 20 = 20$
6. Change in quantity $\Delta Q = Q_2 - Q_1 = 400 - 600 = -200$
7. Average price $\frac{P_1 + P_2}{2} = \frac{20 + 40}{2} = 30$
8. Average quantity $\frac{Q_1 + Q_2}{2} = \frac{600 + 400}{2} = 500$

$E_d = \frac{-200 / 500}{20 / 30} = \frac{-0.4}{0.6667} = -0.60$

These are the step-by-step calculations for each part of the question.