Lately, headlines seem to focus on big companies that pay no corporate taxes. However, most of those big companies are still paying payroll taxes. So, have these big companies actually paid their fair share? Americans have their own tax burdens as well. How do we measure a fair tax for all incomes? How do people define what “fair” means? Join James Harrigan and Antony Davies as they cover progressive/regressive taxes, sales taxes, sin taxes, and more on this week’s episode of Words & Numbers.

Show Notes:

New York may ban glass and steel buildings

Scientists discover how to convert blood to Type O

Foolishness of the week:

Treasury: US may have to stop borrowing

Topic of the week: Taxes

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Thought Experiment: Should the government tax buyers or sellers?

Consider the following three scenarios. In all three scenarios, a seller sets a price and a buyer decides, based on the price, how many units to buy. The number of units the seller sells varies depending on the price the seller charges:

Units sold = 100 - Price per unit

For simplicity (and no meaningful reduction in realism) suppose that it costs the seller $40 for each unit the seller sells. In the first scenario there is no tax. This is a baseline against which we can compare the scenarios in which there is a tax. In the second scenario, the government imposes a $6 per unit tax on the seller. For each unit the seller sells, the seller must pay (in addition to the $40 cost of selling the unit) $6 to the government. In the third scenario, the government imposes a $6 per unit tax on the buyer. For each unit the buyer sells, the buyer must pay the seller’s price to the seller plus an additional $6 to the government.

In each scenario, you can see the price that maximizes the seller’s profit. This is the price the seller will charge in that scenario. You can check the work by choosing a different price. You’ll see that any price other than the one shown results in less profit. At the end of each scenario, you see the final result: how much the buyer pays per unit and how much the seller receives per unit. Compare those results across the three scenarios to see something remarkable.

Scenario 1: No Sales Tax

Profit is maximum when the seller charges $70 per unit.

Units sold = 100 - 70 = 30

Sales = $70 x 30 units = $2,100

Cost of goods sold = $40 x 30 units = $1,200

Profit = $2,100 - $1,200 = $900

→ Buyer pays $70 per unit

→ Seller receives $70 per unit

Tax the Seller $6 per Unit Sold

Profit is maximum when the seller charges $73 per unit.

Units sold = 100 - 73 = 27

Sales = $73 x 27 = $1,971

Cost of goods sold = $40 x 27 + $6 x 27 = $1,242

Profit = $1,971 - $1,242 = $729

→ Buyer pays $73 per unit

→ Seller receives $73 per unit less $6 per unit tax = $67 per unit

→ Compared to No Tax, buyer pays $3 per unit more and seller receives $3 per unit less

Tax the Buyer $6 per Unit Purchased

Profit is maximum when the seller charges $67 per unit.

Units sold = 100 - 67 = 27

Sales = $67 x 27 = $1,809

Cost of goods sold = $40 x 27 = $1,080

Profit = $1,809 - $1,080 = $729

→ Buyer pays $73 per unit ($67 per unit plus $6 per unit tax)

→ Seller receives $67 per unit

→ Compared to No Tax, buyer pays $3 per unit more and seller receives $3 per unit less

Conclusion

It doesn’t matter whether the government taxes the buyer or the seller, they end up sharing the tax burden in the same way. The government decides from whom the tax is collected. The market determines who actually pays the tax.

No Tax

Tax the Seller

Tax the Buyer

Sale price

$70

$73

$67

Price seller receives (net of tax)

$70

$73 - $6 = $67

$67

Price buyer pays (including tax)

$70

$73

$67 + $6 = $73

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#142 - Fragen und Antworten (Teil 2)