Partial vs General Equilibrium

Excess demand constraints Excess demand constraints INV

PX RENT WORK

GDP=( + )/ + GDP=(WORK+RENT+GOVT)/PX+INV

LS

LD= LD=LS

KS

KD= KD=KS

0 )

(swLS+srKS −PX⋅INV = (swLS+srKS+GSAV)−PX⋅INV =0

GDP= nominal production, LD= labour demand, KD= capital demand, LS= labour supply, KS= capital supply, r= rental rate of capital, w=wage rate, WORK= nominal workers’ consumption, RENT= nominal capitalists’ consumption, sw= saving propensity for workers, sr= saving propensity for capitalists, INV=

real investments, PX= output price, GOVT= nominal government consumption, tw= direct tax rate on workers, tr= direct tax rate on capitalists, GSAV= nominal government saving.

Figure 1: A diagrammatical representation

A

B

C

D

E

F

Supply

Demand

q^* qd

Pd

P^*

Ps

To better define the differences and which elements are captured by the two approaches, we concentrate on the case of a new import tax on a specific good. Let us suppose this good is called A, which is both produced domestically and imported. This analysis is based on the usual downward sloping demand curve and the upward sloping supply curve in the space (P,q). The diagrammatical description is provided in graph 1 according to the contemporary version of the theory. As it is defined, the demand curve represents the willingness of customers to pay, in other words each combination (P, q) represents the price P consumers are willing to pay for the quantity q. The supply curve represents, given the price, the total amount of output firms want in order to supply in the market. In this case these curves represent the demand and supply at the national level for good A. At the starting point price equals P^* and the quantity is q^*. However, the introduction of the tariff, with a rate tm, increases the prices up to the level P(1+tm), here defined as Pd. As a consequence, demand has been reduced to level qd. Because of the higher price, consumers reduce their consumption and at the same time producers reduce their surplus. In fact, at the quantity level qd, they obtain only Ps as price. The wedge between Ps and Pd represents the exact tax rate imposed by the Government.

The economy reaches a new equilibrium position with a lower marketed quantity and a higher price. Usually this framework is employed to answer questions like: who gains from the imposition of an import tax? How much is the loss of consumers?

To answer these, and similar questions, we have to analyse what is commonly defined as the “little triangles” (von Arnim, Taylor, 2006). The fundamental concepts are the consumer and the producer surpluses. The former consists of the benefit accumulated by consumers in the market from buying the good, while the latter is the benefit accumulated by producers selling the same good. To solve the welfare calculations we refer to the graph below.

Source: Taylor, von Arnim (2006)

Graphically, the consumer surplus is the area below the demand curve delimited by the vertical axis and price level. The producer surplus is the area above the supply curve. In our graph, at the starting point the consumer’s surplus is the area (A+B+E) while the producer’s surplus is (C+D+F).

In this situation there are only these two agents but in a situation where a tax is imposed, Government is now put into the mix and its impact on the equilibrium must be studied.

Therefore, after the tax imposition, we have to calculate three welfares. Consumer’s surplus is reduced to area A and producer’s surplus to area D. The welfare loss is now equal to (B+C+E+F). However, this loss is in part gained by Government as tariff revenue (area B+C).

Therefore, the private sector’s loss is partially the public sector’s revenue.

As the schematic representation below in box 2 shows, a comparison between the starting point, a position of equilibrium, and the after-tax scenario demonstrates that there are two areas (E+F) which are not gains either for government or private sector. This area is usually referred to as “deadweight loss” and it is composed of the two “little triangles”, to suggest that both private actors lose after the tax imposition.

In their critique on partial analysis, Taylor and von Arnim (2006) stress that the existence of a collective demand function as a collective supply function may be realistic if and only if we assume producers and consumers act with the same rationale and the same behaviour. Their existence, furthermore, depends upon the assumption of a representative agent. This approach is plausible if each agent has a unitary income elasticity of demand and their income is fixed and independent of prices. Plus, producers and consumers have different taste and technologies available so it is not easy to define which is the maximizing agent. These critiques are reasonable and demonstrate lack in this approach both in its methodological and philosophical aspects.

Turning to our comparison between PE and GE, it is easy to present situations that will

Box 2: The welfare calculation

Ex-ante Ex-post

Consumer’s surplus A+B+E A

Producer’s surplus C+D+F D

Government surplus - B+C

A+B+C+D+E+F A+B+C+D

Deadweight loss E+F

Using the partial equilibrium theory we have solved issues on the specific market A.

However, if we add a complementary good, B, the analysis becomes more complex. For instance, there should be a change in the compositional demand of the two goods. In other words, if the price of A increases, it is impossible to determine how consumers will decide to allocate their income. Furthermore, when a change in the demand pattern happens, firms consequently have to modify their production plans. Therefore a change in employment levels in the different sectors may occur. Finally, to give an example, the complementary good’s price may move and consumers may shift their consumption to another good. We must only imagine the presence of a complementary good to complicate the picture. If we continue to consider other aspects or interactions, partial equilibrium analysis becomes less useful to describe the effects of a shock.

To sum up, partial equilibrium analysis may be an accurate way to evaluate economic shocks in a single market even if it is small compared to the rest of the economy. This does mean that the effects on this market have no relevant secondary effect on the whole economic structure. But, if the market is considerably large and if it is correlated with many other markets, partial equilibrium is not capable of capturing all the relevant effects and its results are not realistic. Ignoring the effects on other markets may be seriously misleading. However, to have a more precise and comprehensive picture of the situation, the general equilibrium approach is usually assumed to be more useful. An example may better clarify the issue: Let us suppose that an economic system produces only two goods, A and B. Then let us suppose that the government decides to levy an import tax on imports of good A. Here, imported goods have a higher price so that domestic production for good A increases. This may divert the production against product B. Moreover, there may be effects on employment and household income with additional effects on demand. This simple example demonstrates that a GE approach is able to pinpoint feedback and effects on flow if a policy changes.