1. Suppose that an increase in the price of carrots from $1.20 to $1.40 per pound raises the amount of carrots that carrot farmers produce from 1.2 million pounds to 1.6 million pounds. Using the midpoint method, what would be the elasticity of supply?
a. 0.50
b. 1.86
c. 0.54
d. 2.00
2. Suppose that the equilibrium quantity in the market for widgets has been 200 per month. Then a tax of $5 per widget is imposed. As a result, the government is able to raise $750 per month in revenue. By how much has the equilibrium quantity of widgets fallen?
a. 25 per month
b. 50 per month
c. 75 per month
d. 100 per month
Answer for 2 is 50
1. To calculate the elasticity of supply using the midpoint method, we use the formula:
Elasticity of Supply = (Percentage change in quantity supplied) / (Percentage change in price)
The percentage change in quantity supplied can be calculated as follows:
Percentage change in quantity supplied = ((Final quantity supplied - Initial quantity supplied) / [(Final quantity supplied + Initial quantity supplied) / 2]) * 100
Given:
Initial price = $1.20 per pound
Final price = $1.40 per pound
Initial quantity supplied = 1.2 million pounds
Final quantity supplied = 1.6 million pounds
Percentage change in quantity supplied = ((1.6 million - 1.2 million) / [(1.6 million + 1.2 million) / 2]) * 100
= (0.4 million / 1.4 million) * 100
= (0.4/1.4) * 100
= 28.57%
The percentage change in price can be calculated as follows:
Percentage change in price = ((Final price - Initial price) / [(Final price + Initial price) / 2]) * 100
Percentage change in price = (($1.40 - $1.20) / [($1.40 + $1.20) / 2]) * 100
= ($0.20 / $1.30) * 100
= (0.20/1.30) * 100
= 15.38%
Using the formula for elasticity of supply:
Elasticity of Supply = (Percentage change in quantity supplied) / (Percentage change in price)
= 28.57% / 15.38%
= 1.857
Therefore, the elasticity of supply, using the midpoint method, is approximately 1.86.
Answer: b. 1.86
2. The tax per widget is $5, and the government is able to raise $750 per month in revenue. We can use this information to calculate the number of widgets sold:
Revenue from tax = Tax per widget * Quantity of widgets sold
$750 = $5 * Quantity of widgets sold
Quantity of widgets sold = $750 / $5
= 150 widgets
Since the equilibrium quantity before the tax was 200 widgets, the equilibrium quantity of widgets has fallen by:
Fall in equilibrium quantity = Initial equilibrium quantity - Quantity of widgets sold
= 200 - 150
= 50 per month
Therefore, the equilibrium quantity of widgets has fallen by 50 per month.
Answer: b. 50 per month
To find the elasticity of supply using the midpoint method, we need to calculate the percentage change in quantity supplied and the percentage change in price.
1. Calculate the percentage change in quantity supplied:
Percentage change in quantity supplied = [(new quantity - old quantity) / ((new quantity + old quantity) / 2)] * 100
= [(1.6 million - 1.2 million) / ((1.6 million + 1.2 million) / 2)] * 100
2. Calculate the percentage change in price:
Percentage change in price = [(new price - old price) / ((new price + old price) / 2)] * 100
= [(1.40 - 1.20) / ((1.40 + 1.20) / 2)] * 100
3. Now, plug in the values into the formula for the midpoint method:
Elasticity of supply = (percentage change in quantity supplied) / (percentage change in price)
Find the correct option by calculating the value of elasticity of supply and matching it with the options provided. The option with the closest value to the calculated elasticity of supply is the correct answer.
For the second question:
To find the change in equilibrium quantity, we need to calculate the quantity reduction caused by the tax.
1. Calculate the revenue raised by the tax: revenue = tax per widget * quantity
$750 = $5 * quantity
2. Solve for quantity:
quantity = $750 / $5
3. Calculate the reduction in equilibrium quantity:
reduction in equilibrium quantity = initial equilibrium quantity - quantity with tax
Find the correct option by calculating the reduction in equilibrium quantity and matching it with the options provided. The option with the closest value to the calculated reduction in equilibrium quantity is the correct answer.