Impact of an Excise Tax or Subsidy on Price (2024)

An excise tax is a tax on a specific commodity. Such a tax may raise the price of the commodity to the consumer and reduce the net price received by the producer. Itgenerally will do both and reduce the amount marketed and purchased. The effects willdepend upon the mechanism which determines the market price and that will depend uponthe market structure; i.e., the extent of competition in the market.

The impact of a tax or subsidy on a protected monopoly is dealt with elsewhere.

Determination of Market Price in a Competitive Market

The Normal Case

The demand function for a market is the relationship between the priceof the commodity and the quantity of it deamanded. Likewise the supplyfunction is the relationship between the price of the commodity andthe quantity of it supplied. The demand and supply functions can berepresented as curves in a graph, such as is shown below.

Let p_eq and q_eq the price and quantity where thedemand and supply curves intersect.Let D(p) be the demand function for the market and S(p) the supply function.If p > p_eq then the quantity demanded is less than thequantity supplied, D(p) < S(p), and the surplus results in the marketprice being bid down. On the other hand if p < p_eq thenthe quantity demanded is greater than the quantity supplied; D(p) >S(p); the resulting shortage causes the bprice to be bid up.

At p_eq the quantity demanded is exactly equal to thequantity supplied and there is no tendency for the price to change. It is,in fact, the equilibrium price. The quantity demanded and supplied atthat price is the equilibrium output, q_eq.

The Impact of an Excise Tax

Suppose a tax of t is imposed upon the commodity and the tax is collectedfrom the producers. One's first expectation would be that the marketprice would increase by the amount of the tax, to (p_eq+t).In this case the producers would still be gettiing p_eq andthus would supply the same amount q_eq. But the quantitydemanded at (p_eq+t) will be less than q_eq and thusthat could not be an equilibrium situation. This shortage would drivethe price down. The new equilibrium would be somewhere betweenp_eq and (p_eq+t).

Algebraically the new equilibrium price for consumers p_c is theprice such that

D(p_c) = S(p_c + t)

Graphically the determination of the new equilibrium price is shown below.

In the above graph P_t represents the price paid by consumers once the taxis imposed. P_t' is the price received by the producers once the tax is imposed.The difference between P_t and P_t is equal to the amount of the tax. The effectof the tax is to shift the supply curve, which is S without the tax, to St.The shift is an upward shift by the amount of the tax, but the upward shiftis the same as a backward shift, a decrease in supply. As can be seen fromthe above graph, the impact of the tax is an increase in the price paid byconsumers and a decrease in the price received by producers. Thus the consumersand producers share the burden of the tax. In this case the burden of thetax is equally shared by the consumers and producers, but that has to do withthe relative slopes of the demand and supply curves. From this graph the loss in consumers' surplus and the loss in producers'surplus may be determined as shown below. The loss in consumers' surplusis shown in pink and the loss in producers' surplus in light blue (cyan).

The combined loss in consumers' and producers' surplus is offset in partby the gain to the government in tax revenue. But the offset is onlypartial; the loss to consumers and producers is greater than the tax revenuegained, as is shown below. The situation is analogous to a car burglarbreaking into a car and doing $500 of damage to get a $50 item. The lossto the car owner is $550 whereas the burglar gets only $50.

The Impact of a Subsidy

Although the analysis of the impact of a tax is important the analysisof the impact of a subsidy is more interesting. The analysis is essentiallythe same, a subsidy merely being a negative tax. The effect of a subsidyis to shift the supply curve downward by the amount of the subsidy. Effectivelythis is an increase in supply. The graph below shows the results of asubsidy on a market.

In the above graph (and following graphs) P_s represents the price paidto consumers after the subsidy is created. P_s' represents the price receivedby the producers, which is the price paid by consumers plus the subsidy.The impact of the subsidy is to lower prices for consumers but to increasethe price received by producers. The benefit of the subsidy is sharedby the consumers and producers in a proportion that depends upon therelative slopes of the demand and supply functions.

The above graph shows the gains in consumers' and producers' surplusesas a result of the subsidy. Although the effect of the subsidy seems beneficial the importantquestion is the cost of the subsidy relative to the benefits. In thegraph shown below the cost of the subsidy to the government is the gray rectangle includingthe colored triangles. The graph shows the balance is negative; i.e., the cost of the subsidyis always greater than the benefits to consumers and producers. This isan important result of analysis.

The deadweight loss of the subsidy is the amount by which the cost ofthe subsidy exceeds the gains in consumers' and producers' surpluses, thetriangles shown in pink and blue. The magnitude of the deadweight loss of a tax or subsidy depends uponthe amount of the tax or subsidy and the change in production that resultsfrom the tax or subsidy. Specifically

Deadweight Loss = (1/2)(amount of tax or subsidy)*ΔQ

where ΔQ is the change in output.

Since the change in output ΔQ is proportional to the amount of the tax orsubsidy the deadweight loss is proportional to the square of the tax orsubsidy. This means that if the tax or subsidy is doubled the deadweightloss increases by a factor of four. If the tax or subsidy is tripled thedeadweight loss increases by a factor of none.

The relationship between the tax rate and the amount of tax revenuecollected is a parabola, a form popularized by Art Laffer.The Laffer Curveshows that beyond a certain point an increase in the tax rate results ina decrease in tax revenue rather than an increase. This relationshipwas popularized as part of the Supplyside Economics of theReagan Administration.

The Economic Effect of a Tax (or Subsidy) is Independent of WhichParty Makes (or Receives) the Payment to (or from) the Government

This is an important implication of the economic analysis of an excisetax that could easily be overlooked. In the previous analysis it wasimplicitly assumed that the producer makes the tax payment to the government.The price received by the producers was equal to the price paid by consumersless the amount of the tax. As a result if we look at the supply functionas the relationship between the price paid by consumers and the quantitysuppled this supply curve shifts vertically upward by the amount of the tax. Thedemand function as the relationship between the price paid by consumersand the quantity demanded remains unchanged.

Suppose the government required consumers to keep track of their purchasesand send a tax payment to the government based on the number of units oftaxable goods purchased. If the graph shows quantities demanded andquantities supplied as a function of the price received by producersthe supply curve would stay fixed and the demand curve would shift verticallydownward by the amount of the tax. This is equivalent to a leftward shift in thein demand resulting in a smaller quantity produced and bought. The pricereceived by the producers would fall as a result of the tax. The pricepaid by consumers, which is the price received by producers plus theamount of the tax, would rise. It will rise by exactly the same amountas the it would rise if the same tax were collected from the producersrather than the consumers.

As a practical matter it is a lot easier for the government to collecttaxes from the sellers (businesses), than from the buyers (consumers).Therefore the government usually imposes taxes are upon the producers ratherthan upon the consumers but the burden on the consumers is exactly thesame.

The same conclusion applies to subsidies. The effect on prices is thesame whether the subsidy payment is made to consumers or producers. Thus ina competitive market for medical services the effect of government reimbursem*ntof medical costs to patients will have the same effect on medical serviceprices as an equal subsidy to the medical service providers.

The Case of a Backward Bending Supply Curve

A backward bending supply curve in the case of labor supply is a perfectlyreasonable phenomenon. If wage rates in a particular occupationreach high enough levels the recipients of those wage rates may decidedto work less rather than more. In effect, the recipients of the high wagerates may choose to take the benefit of the high pay in terms of moreleisure time and hence less work.

An equilibrium of the wage rate in the backward bending portion of thesupply curve is a completely legitimate economic equilibrium. But theeffect of an excise tax or subsidy in such a market is quite surprising andcontrary to what was intended.

First we should examine whether the intersection of the demand andsupply curves for this type of market is a stable equilibium. That isto say, if the price is below the equilibrium does quantity demandedexceed quantity supplied and result in a shortage that drives up theprice and if the price is above the equilibrium does the quantity suppliedexceed the quantity demanded and result in a surplus on the market thatdrives the price down? As shown in the graph below it is shown that theseconditions do prevail and therefore the equilibrium is stable.

When a tax is imposed in a market with a backward-bending supply curvethe effect on the equilibrium prices for the consumers and producers issurprising, as is shown in the diagram below.The tax results in avertical upward shift in the supply curve by the amount of the tax.

Likewise the effect of a subsidy in a market with a backward-bendingsupply curve is contrary to expectations, as is shown below.The subsidy results in avertical downward shift in the supply curve by the amount of the subsidy.