Question

Suppose that the local government of Tulsa decides to institute a tax on soda producers. Before the tax, 35,000 liters of soda were sold every week at a price of $11 per liter. After the tax, 30,000 liters of soda are sold every week; consumers pay $14 per liter, and producers receive $6 per liter (after paying the tax).

The amount of the tax on a liter of soda is
$
per liter. Of this amount, the burden that falls on consumers is
$
per liter, and the burden that falls on producers is
$
per liter.

Answer 1

The amount of the tax per liter of soda is $8.

The burden that falls on consumers is $0 per liter, and the burden that falls on producers is $3 per liter.

Tax Amount:

The tax is the difference between the price paid by consumers after the tax and the amount received by producers after the tax. Mathematically, it is given by:

`\[ \text{Tax Amount} = \text{Consumer Price after Tax} - \text{Producer Amount after Tax} \] \[ \text{Tax Amount} = \$14 - \$6 \] \[ \text{Tax Amount} = \$8 \]`

Burden on Consumers:

The burden on consumers is the difference between the price paid by consumers after the tax and the original price. Mathematically, it is given by:

`\[ \text{Burden on Consumers} = \text{Consumer Price after Tax} - \text{Original Price} \] \[ \text{Burden on Consumers} = \$14 - \$11 \] \[ \text{Burden on Consumers} = \$3 \]`

Burden on Producers:

The burden on producers is the difference between the original price and the amount received by producers after the tax. Mathematically, it is given by:

`\[ \text{Burden on Producers} = \text{Original Price} - \text{Producer Amount after Tax} \] \[ \text{Burden on Producers} = \$11 - \$6 \] \[ \text{Burden on Producers} = \$5 \]`

Therefore, the amount of the tax on a liter of soda is $8, with $3 falling on consumers and $5 falling on producers.

Complete question:

Tulsa decides to institute a tax on soda producers. Before the tax, 35,000 liters of soda were sold every week at a price of $11 per liter. After the tax, 30,000 liters of soda are sold every week; consumers pay $14 per liter, and producers receive $6 per liter (after paying the tax).

The amount of the tax on a liter of soda is $ per liter.

Of this amount, the burden that falls on consumers is $ per liter, and the burden that falls on producers is $ per liter.

Answer 2

To find the amount of the tax per liter of soda, we can use the information given in the problem:

- Before the tax, 35,000 liters of soda were sold every week at a price of $11 per liter.
- After the tax, 30,000 liters of soda are sold every week; consumers pay $14 per liter, and producers receive $6 per liter (after paying the tax).

The total revenue from soda sales before the tax was:

35,000 liters × $11/liter = $385,000 per week

The total revenue from soda sales after the tax is:

30,000 liters × $14/liter = $420,000 per week

The difference in revenue is due to the tax. Let's call the amount of the tax per liter of soda "t". Then we have:

(30,000 liters × $6/liter) + (30,000 liters × t/liter) = $420,000 per week

Simplifying and solving for t, we get:

t = ($420,000 per week - $180,000 per week) / 30,000 liters

t = $8 per liter

Therefore, the amount of the tax per liter of soda is $8.

To find the burden that falls on consumers and producers, we can use the price of soda before and after the tax. Before the tax, consumers paid $11 per liter and producers received $11 per liter. After the tax, consumers paid $14 per liter and producers received $6 per liter. The difference in price is due to the tax. Let's call the burden that falls on consumers "bc" and the burden that falls on producers "bp". Then we have:

bc + bp = $14 - $11

bc + bp = $3 per liter

And we know that:

bp = $11 - $6 = $5 per liter

Substituting this value into the previous equation, we get:

bc + $5 per liter = $3 per liter

bc = $3 per liter - $5 per liter

bc = -$2 per liter

Since the burden that falls on consumers is negative, we can say that the burden falls entirely on producers, who bear the full $3 per liter increase in price due to the tax.

Therefore, the burden that falls on consumers is $0 per liter, and the burden that falls on producers is $3 per liter.