Market Impact of Payroll Tax At the bottom of page 157 the author starts with the sentence, “This result illustrates a principle that is worth remembering: The true incidence of the payroll tax has little to do with the way the tax law is written or the way the tax is collected. …” (finish reading that paragraph, please!) We explore this idea here. 1

Tax on suppliers or demanders of labor In a competitive labor market suppliers make the decision to enter the labor market based on their preferences for leisure and consumption, while they are mindful of the wage they can earn. Demanders of labor are mindful of productivity and the cost of production that results. The interaction of supply and demand in a competitive market determines the wage and the quantity traded. Let’s explore what happens in the labor market with regards to the wage and the quantity traded when the government enters the market and taxes either the demanders or suppliers in the market. 2

Tax on demanders of labor $ E demand before the tax demand after the tax W1 W1 - t W2 W2 - t E1 E2 3

Tax on demanders of labor On the previous screen firms demanded E1 units of labor because, when they pay out W1 per worker, E1 is the amount of labor that maximizes the profit of the firm. A similar story is told about E2 and W2. Say the tax is a lump sum, t per worker. The economic story here is that with the tax the firms will still take, for example, E1 when they pay out W1. But now the W1 will not all go to the worker. Of the W1, t will go to the government and W1 - t will go to the worker. The firm maintains profit by adjusting what it will give to workers. Same story holds at E2, W2 This effectively drops the demand curve down by the amount of the tax. 4

Tax on suppliers of labor $ E W1 + t W1 E1 Sat Sbt 5

Tax on suppliers of labor On the previous screen people supplied E1 units of labor because, when they get paid W1 per worker, E1 is the amount of labor that maximizes the utility of the worker Say the tax is a lump sum, t per worker. The economic story here is that with the tax the people will still supply, for example, E1 when they get paid and keep for themselves W1. But in order to get to keep W1, W1 + t must be obtained. The worker then pays t to Caesar and keeps W1. The worker maintains utility by adjusting what it must get from employers. This effectively raises the supply curve up by the amount of the tax. 6

Market impact Sbt $ Dbt Sat Dat E Wbt W wk W fp Eat Ebt subscript bt means before tax at means after tax wk means worker keeps fp means firm pays 7

subliminal slide push this line segment into the x until it gets stuck 8

subliminal slide 2 like this 9

reason for subliminal slides Where the line segment gets stuck is a point of reference for us. Say the line segment is the amount of the tax. If suppliers get taxed, the supply shifts up by the tax and the new supply curve will meet the existing demand curve right at the top of the line segment. If demanders get taxed, the demand curve shifts down by the tax and the new demand will meet the existing supply curve right at the bottom of the line segment. When we explore the market impact we either tax demanders or suppliers, but not both at the same time. 10

Market impact When you look back at slide 7 the equilibrium wage and labor traded in the market before the imposition of any tax is Wbt and Ebt, respectively. (Can you say why?) Now, say suppliers are taxed. The supply shifts up by t, the amount of the tax. The market wage becomes Wfp and the amount traded in the market is Eat. Workers collect Wfp and pay t to the government. Workers keep Wfp - t = Wwk Now, say demanders are taxed. The demand shifts down by t, the amount of the tax. The market wage becomes Wwk and the amount traded in the market is Eat. Firms pay workers Wwk and pay t to the government. In total firms pay Wfp = Wwk + t. 11

market impact Either way the tax is set up: Firms pay Wfp and workers get Wwk; the tax is Wfp - Wwk = t per worker; the amount employed after the tax is Eat; the government revenue is t times Eat. Note before the tax the worker received Wbt and after the worker (still employed) is paid Wwk. Wbt - Wwk is the part of the tax paid by the worker in terms of a lower wage. Note before the tax the firm paid Wbt and after it pays Wfp. Wfp - Wbt is the part of the tax paid by the firm in the form of higher payment. 12

Deadweight loss of tax Sbt $ Dbt Sat Dat E Wbt W wk W fp Eat Ebt subscript bt means before tax at means after tax wk means worker keeps fp means firm pays A B C D E F 13

DWL – deadweight loss of tax 14 On the previous slide I reproduced what I had before and I added some information. Before the tax with Bdt and Sbt the market outcome is Wbt and Ebt. Areas A + B + C add up to producer surplus and Areas D + E + f add up to worker surplus. (You can see these areas are triangles and rectangles and if you knew values you could come up with numerical values for the surpluses because rectangle area = base times height and triangle are = half of base times height.)

DWL 15 When viewed from the point of view of the original supply and demand, either tax means 1) the firms as demanders of labor end up paying Wfp and thus producer surplus goes down by areas B and C, and 2) The workers as suppliers of labor end up receiving Wwk and thus worker surplus falls by area D and E. So, it appears that total surplus from the tax falls by B + C + D + E. But, areas B and D actually makes up the tax revenue and thus represent a gain that balances out the loss to the firms and workers. The net loss in surplus is called the deadweight loss and equals the areas C and E. Note these areas are above the loss in employment amount Ebt – Eat. So, the DWL is a measure of the loss in employment due to the tax.