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# 经济代写|宏观经济学代考Macroeconomics代写|ECON1120

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## 经济代写|宏观经济学代考Macroeconomics代写|Using Consumer and Producer Surplus to Find the Welfare Effects of a Tax

To simplify the explanation of elasticity and the tax incidence, we will not complicate the illustration by shifting the supply curve (tax levied on sellers) or demand curve (tax levied on buyers) as we did in Section 6.4. We will simply show the result a tax must cause. The tax is illustrated by the vertical distance between the supply and demand curves at the new after-tax output-shown as the bold vertical line in Exhibit 1. After the tax, the buyers pay a higher price, $P_B$, and the sellers receive a lower price, $P_S$; and the equilibrium quantity of the good (both bought and sold) falls from $Q_1$ to $Q_2$. The tax revenue collected is measured by multiplying the amount of the tax times the quantity of the good sold after the tax is imposed $\left(T \times Q_2\right)$.

In Exhibit 2, we can now use consumer and producer surpluses to measure the amount of welfare loss associated with a tax. First, consider the amounts of consumer and producer surplus before the tax. Before the tax is imposed, the price is $P_1$ and the quantity is $Q_1$; at that price and output, the amount of consumer surplus is area $a+b+c$, and the amount of producer surplus is area $d+e+f$. To get the total surplus, or total welfare, we add consumer and producer surpluses, area $a+b+c+d+e+f$. Without $a$ tax, tax revenues are zero.

After the tax, the price the buyer pays is $P_B$, the price the seller receives is $P_s$, and the output falls to $Q_2$. As a result of the higher price and lower output from the tax, consumer surplus is smaller-area a. After the tax, sellers receive a lower price, so producer surplus is smaller-area f. However, some of the loss in consumer and producer surpluses is transferred in the form of tax revenues to the government, which can be used to reduce other taxes, fund public projects, or be redistributed to others in society. This transfer of society’s resources is not a loss from society’s perspective. The net loss to society can be found by measuring the difference between the loss in consumer surplus ( $a r e a b+c$ ) plus the loss in producer surplus (area $d+e$ ) and the gain in tax revenue $($ area $b+d)$. The reduction in total surplus is area $\mathrm{c}+\mathrm{e}$, or the shaded area in Exhibit 2. This deadweight loss from the tax is the reduction in producer and consumer surpluses minus the tax revenue transferred to the government.

## 经济代写|宏观经济学代考Macroeconomics代写|Elasticity and the Size of the Deadweight Loss

The size of the deadweight loss from a tax, as well as how the burdens are shared between buyers and sellers, depends on the price elasticities of supply and demand. In Exhibit 3(a) we can see that, other things being equal, the less elastic the demand curve, the smaller the deadweight loss. Similarly, the less elastic the supply curve, other things being equal, the smaller the deadweight loss, as shown in Exhibit 3(b). However, when the supply and/or demand curves become more elastic, the deadweight loss becomes larger because a given tax reduces the quantity exchanged by a greater amount, as seen in Exhibit 3(c). Recall that elasticities measure how responsive buyers and sellers are to price changes. That is, the more elastic the curves are, the greater the change in output and the larger the deadweight loss.

Elasticity differences can help us understand tax policy. Goods that are heavily taxed, such as alcohol, cigarettes, and gasoline, often have a relatively inelastic demand curve in the short run, so the tax burden falls primarily on the buyer. It also means that the deadweight loss to society is smaller for the tax revenue raised than if the demand curve were more elastic. In other words, because consumers cannot find many close substitutes in the short run, they reduce their consumption only slightly at the higher after-tax price. Even though the deadweight loss is smaller, it is still positive because the reduced after-tax price received by sellers and the increased after-tax price paid by buyers reduces the quantity exchanged below the previous market equilibrium level.

# 宏观经济学代写

## Matlab代写

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