Taxes and their effects on markets

TAXES ON SELLERS

Consider the market for slices of pizza with equilibrium price equal to 3$ and the equilibrium quantity also equal to 3. Suppose the government decides to impose a tax on sellers of 1$ for every slice of pizza they sell. The tax reduces revenues for sellers. This means that, for any given price, a lower quantity will be supplied. The supply curve will, therefore, shift to the left in a parallel fashion. In order to compensate for the decrease in revenues the supply curve has to be moved upward by exactly the amount of taxes imposed, which is in this case 1 (notice that moving the supply curve to the left or upward has the same result but mathematically it is more convenient to consider an upward shift). The equilibrium price rises to 3,5 while the equilibrium quantity decreases to 2,5, so the market shrinks in size. Obviously buyers are worse off because they have to pay a higher price to get their slice of pizza. Also sellers are worse off because their revenues decrease: before they could sell 3 slices at 3$ so revenues were 3*3=9, now they can sell 2,5 slices at 3,5$ but, of these 3,5$, 1$ has to be given to government and, therefore, revenues are 2,5*2,5=6,25. The tax has made both consumers and producers worse off: buyers pay more but sellers earn less.

TAXES ON BUYERS

Suppose that this time a new law imposes to customers to send 1$ to the government each time they buy a slice of pizza. This time the supply curve is not affected and thus it does not move. Customers on the contrary are affected by the new law. Now buying a slice of pizza becomes more expensive. This means that, for any given price, a lower quantity will be demanded. The demand curve will, therefore, shift to the left in a parallel fashion. In order to compensate for the increase in expenses, the demand has to move downward by exactly the amount of the tax imposed, which is in this case 1 (notice that moving the demand curve to the left or downward has the same result but mathematically it is more convenient to consider a downward shift). The equilibrium price falls to 2.5 and the equilibrium quantity falls to 2.5, so the size of the market is once again reduced. Buyers are worse off because now for each slice of pizza they have to pay 2.5$ to sellers and 1$ to government. Also sellers are worse off because, before the law, their revenues were 3*3=9 and, after the law is applied, their revenues are 2.5*2.5= 6.25. the tax has made both consumers and sellers worse off: buyers pay more and sellers earn less.

This clearly shows that whether the government imposes a tax on buyers or sellers the result is the same, the only thing that changes is who is responsible to send the money to the government.

WHO PAYS TAXES

The incidence of a tax shows how the burden of the tax is distributed among the two sides of the market: demand and supply. As we saw both buyers and seller are affected negatively by the tax but rarely they are affected in equal proportions. Suppose that you have a market where demand is inelastic and supply is elastic, in this case, because of inelasticity (did you miss the lecture on elasticity?), people will have to buy the good even if the price raises and so the demand side will be affected more than the supply side. In the opposite case, where there is a market with elastic demand and inelastic supply, sellers are not responsive to changes in the price and, therefore, the supply side will be affected more than the demand side. This shows that the burden of the tax affects more the side of the market which is less elastic.

THE EFFECTS OF A TAX

Because we said that is indifferent imposing a tax on buyers or on sellers, we can calculate the “revenues” of the government when imposing a tax by considering the area rectangle, with height the amount of the tax, that is created between the demand and supply curves. The width of the rectangle represents the quantity of the good on which the tax is applied. Therefore the tax revenue for the government is TxQ.

Let’s divide the area between the two curves is smaller parts as in the picture. Remember that, without a tax, total surplus in the market is given by all the area between the two curves. It is divided into total consumer surplus which is given by area A+B+C and total producer surplus which is given by area F+D+E. After the tax, B+D compose the tax revenue for the government and, therefore, it is taken away from the market surplus. In the end consumer surplus is given only by area A and total producer surplus is given only by area F. But wat about area E and C? They were part of the consumer (C) and producer (E) surpluses but now they are not. They are not part of the tax revenue either. They represent therefore a deadweight loss. No one can exploit that part of the market when a tax is applied because the tax itself prevents buyers and sellers to gain from trading in the market. This happens because a tax maxes goods more expensive for consumers while reducing at the same time revenues for sellers. If no trade takes place also government will not collect any money. A deadweight loss represents therefore a loss for everyone.

HOW ELASTICITY OF SUPPLY AND DEMAND CAN AFFECT DEADWHEIGHT LOSS

The deadweight loss, as said, represents the fact that, when a tax is applied, some trade in the market will not

take place and so the size of the market is reduced. Remember from the lecture on elasticity that elasticities of demand and supply represent how much that specific side of the market will react when prices change. An elastic demand or supply (E>1) means that the side of the market we are considering is highly responsive to a change in price while an inelastic demand or supply (E<1) means that the side of the market we are considering is not very responsive to a change in price. Because a tax makes trading in the market more expensive both for consumers and producers, in a market where both supply and demand are elastic, the deadweight loss will be much greater than in a market where one of the two is elastic and the other is not or worse both sides are inelastic.

THE SIZE OF THE TAX LARGELY AFFECTS THE DEADWEIGHT LOSS AND THE TAX REVENUE

When a tax increases the deadweight loss created increases faster than the tax itself. This is because the deadweight loss is represented by the area of the triangle having as a base the amount of the tax and as height the distance between the equilibrium point and the base of the triangle. When the amount of a tax is doubled not only the base of the triangle is doubled but the height doubles as well. This means that doubling a tax increases the deadweight loss to 4 times its original value. Not only increasing a tax could be harmful for producers and consumers, but for government as well. This is because, as deadweight loss increases, the size of the market (quantities traded) decrease and therefore there are less goods taxed. When a tax is low or non existent, increasing it will cause a rise in the revenues for government. When the tax is too high few trades will take place and therefore also government revenues will fall. This relationsh between the tax size and tax revenues is depicted by a graph called the Laffer curve.