5520_l_15_tax incidence © Allen C. Goodman, 2015 11/8/2018 WHO REALLY PAYS? Tax Incidence © Allen C. Goodman, 2015

What has been happening Over time, the share of output generated from the relatively less cyclically sensitive service-producing industries has risen modestly in comparison with relatively larger cyclically sensitive goods-producing industries. So, as the share of services has risen, the share (and possibly the amount) of goods-based sales taxes has fallen.

Tax Bites

Short-Run and Long-Run Impacts Why drawn like this? $ D S S' Look at SR supply elasticities? Look at SR demand elasticities? What is impact of 6% tax on services? P2 Total Tax Rev. DW is small P1 Total Sales Q2 Q1 Quantity

Long-Run Impacts Look at LR supply elasticities? Supply more elastic $ D S S'' S' Look at LR supply elasticities? Look at LR demand elasticities? What is impact of 6% tax on services? D'' Demand more elastic P2 Tot. Tax Rev. P1 Tot Sales Q2 Q1 Quantity

Long-Run Impacts What is net impact as drawn? $ D S S'' S' What is net impact as drawn? P3 < P2 because demand is more elastic TR? Depends on whether price ↑ (leading to ↑ in tax per unit) by greater % than quantity ↓. Probably ↓. D'' P2 P3 New Tax Rev. Tot. Tax Rev. P1 Tot Sales Q3 Q2 Q1 Quantity

What happens in parallel markets? e.g. Michigan/Ohio SR? Let’s look at cigarettes. Michigan and Ohio sellers are both price takers. Why? OH $ $ MI D'M DM DO PM+ t Taxes PM PO Q q Q2 Q1 q1

Parallel Market e.g. Michigan/Ohio Let’s look at cigarettes. Michigan and Ohio are both price takers. Why? LR? MI OH $ $ D'M DM DO D'O PM+ t Taxes PM PO Q Q Q'2 Q2 Q1 q1 q2

A Model of a Michigan Service Tax 1 = goods produced nationally– examples? 2 = goods produced locally – examples? T = Taxes Collected by Michigan T = National sector taxes + Local Sector taxes T = t1 p1 Q1 (t1, t2, p1, p2, y) + t2 p2 Q2 (t1, t2, p1, p2, y) y = p1 Q1 + p2 Q2 + - + - + What happens if we establish (increase) taxes on local goods, services?

What will the Full Impact of a tax on local goods be? Lots of things happen!! Prices of local goods ,   in quantity demanded of local goods.  in demand for national goods. What will be the TAX IMPACT and who will pay it?

What will the Full Impact of a tax on local goods be? dT/dt2 = p2 Q2 + t2 p2 (dQ2/dt2) + t2 p2 (dQ2/dp2 ) (dp2/dt2 ) + t1 p1 (dQ1/dt2 ) Less local goods sold! But it Is now taxed. Higher prices, Less sold. More taxes on Substitutes.

What will the Full Impact of a tax on local goods be? dT/dt2 = p2 Q2 + t2 p2 (dQ2/dt2) + t2 p2 (dQ2/dp2 ) (dp2/dt2 ) + t1 p1 (dQ1/dt2 ) dT/dt2 = p2 Q2 + t2 (dQ2/dt2 ) (Q2/Q2) p2 + (Q2/Q2)(p2/p2) t2 p2 (dQ2/dp2 ) (dp2/dt2 ) + (t2/t2) (Q1/Q1) t1 p1 (dQ1/dt2) dT/dt2 = p2 Q2 + dQ2/dt2 (t2 /Q2) (p2 Q2) + p2 Q2 [(dQ2/dp2) (p2/Q2)] [(dp2/dt2) (t2/p2)] + (t1/t2)(p1Q1) (dQ1/dt2) (t2/Q1) dT/dt2 = p2 Q2 + Elas Q2t2 (p2 Q2) + p2 Q2 (Elas Q2p2) (Elas p2t2) + (t1/t2)(p1Q1) (Elas Q1t2) dT/dt2 = p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+ p1Q1 (t1/t2) (Elas Q1t2)

A Model of the Service Tax + or - ? + or - ? + or - ? dT/dt2 = p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+ p1Q1 (t1/t2) (Elas Q1t2) + or - ? KEY POINT --- There are LOTS of Impacts!

A 6% Service Tax This is a one UNIT  in tax. We want 0.06 of that. t2 = 0.06 dT/dt2 = p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+ p1Q1 (t1/t2) (Elas Q1t2) 0.06* (dT/dt2) = 0.06 * p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+ 0.06 * t1p1Q1 (Elas Q1t2) Elas Tt2 = s2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2) + s1 * Elas Q1t2 ; s1 = t1p1Q1/T; s2 = t2p2Q2/T.

A 6% Service Tax t2 = 0.06 dT/dt2 = p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+ p1Q1 (t1/t2) (Elas Q1t2) 0.06* (dT/dt2) = 0.06 * p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+ 0.06 * p1Q1 (t1) (Elas Q1t2) Elas Tt2 = s2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2) + s1 * Elas Q1t2 ; s1 = t1p1Q1/T; s2 = t2p2Q2/T. 6% of original sales of Q2 Change in sales of Q1