Suppose the price of widgets falls from $7 to $5 and consumption of widgets rises from 15 widgets a month to 25 widgets. Calculate your price elasticity of demand of widgets. What can you say about your price elasticity of demand of widgets? Is it Elastic, Inelastic, or Unitary Elastic? Why? Use the Midpoint formula and please show your work.

(a) Price Elasticity of demand of widgets

= (Change in Quantity of demand X/Original Quantity of demand X) divided by (Change in price of X/Original Price of X)
Change in Quantity = 15 - 25 = -10
Original Quantity = 25
Change in Price = (7 - 5) = 2
Original Price = 7
= (-10 / 25) / (2 / 7) = - 1.4
(b) As stated by the law of demand, when the price of a goods falls, quantity demand rises. The price elasticity of demand of widgets is greater than 1 so it is relatively elastic.
(c) I Demand is elastic if a specific percentage change in price results in a larger percentage change in quantity demanded. In such cases, Ed will be greater than 1. t is elastic.
Ed= (Change in Quantity/Sum of Quantities/2) divided by (Change in price/sum of price/2)
= -10/(40/2) / -2/(12/2)
= (-10/20) / (-2/6)
= -0.5/-0.3
= 1.5

Elastic

To calculate the price elasticity of demand using the midpoint formula, we need the following information:

Initial price (P1) = $7
Final price (P2) = $5
Initial quantity demanded (Q1) = 15 widgets
Final quantity demanded (Q2) = 25 widgets

The midpoint formula for calculating price elasticity of demand is:

Elasticity = (ΔQ / ((Q1 + Q2) / 2)) / (ΔP / ((P1 + P2) / 2))

First, let's calculate the percentage changes in quantity demanded and price:

ΔQ = Q2 - Q1 = 25 - 15 = 10
ΔP = P2 - P1 = 5 - 7 = -2 (note the negative sign, as prices decreased)

Now, let's find the average quantity and price:

(Q1 + Q2) / 2 = (15 + 25) / 2 = 20
(P1 + P2) / 2 = (7 + 5) / 2 = 6

Substituting the values into the formula:

Elasticity = (ΔQ / ((Q1 + Q2) / 2)) / (ΔP / ((P1 + P2) / 2))
= (10 / 20) / (-2 / 6)
= 0.5 / (-0.33)
≈ -1.515

Since the calculated price elasticity of demand is greater than 1, it is considered elastic. This means that the demand for widgets is responsive to changes in price. A 1% decrease in price leads to a more than 1% increase in the quantity demanded.

To calculate the price elasticity of demand using the midpoint formula, you need the following equation:

Price elasticity of demand = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))

Where:
Q1 = Initial quantity demanded
Q2 = New quantity demanded
P1 = Initial price
P2 = New price

Given:
Q1 = 15 widgets
Q2 = 25 widgets
P1 = $7
P2 = $5

Let's plug these values into the formula:

Price elasticity of demand = ((25 - 15) / ((25 + 15) / 2)) / (($5 - $7) / (($5 + $7) / 2))

Simplifying,

Price elasticity of demand = (10 / (40 / 2)) / (-$2 / ($12 / 2))
Price elasticity of demand = (10 / 20) / (-$2 / $6)
Price elasticity of demand = 0.5 / (-1/3)
Price elasticity of demand = -1.5

The price elasticity of demand for widgets is -1.5.

Now, let's determine the type of elasticity based on this value:
- If the absolute value of the elasticity is greater than 1, it is considered elastic.
- If the absolute value of the elasticity is less than 1, it is considered inelastic.
- If the absolute value of the elasticity is exactly 1, it is considered unitary elastic.

Since the elasticity value obtained is -1.5 (which is greater than 1), the price elasticity of demand of widgets is elastic.

Explanation: When the price of widgets decreased from $7 to $5, the quantity demanded increased from 15 widgets to 25 widgets, indicating that consumers are highly responsive to changes in price. The elasticity value of -1.5 indicates that for every 1% decrease in price, the quantity demanded increases by 1.5%. This indicates a relatively elastic demand, suggesting that the change in price has a more significant impact on the quantity demanded.