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Applied General Equilibrium Analysis


Definition

Applied General Equilibrium (AGE) Analysis:


Comparing with AGE analysis, the limitations of partial equilibrium (PE) analysis


PE example: subsidy

Consider an example: subsidy on food production


From PE aspect, we only consider supply and demand change of this good (food) (single market), assuming all possible equilibrium on the single market can be produced and consumed.


This PE example is equivalent to a supply-demand figure and we add a subsidy for producer


In functional form, it would be:
PS = PM*TO: producer's price = market price * tax ratio (> 1 because it is a subsidy), producer earns more.
QO = S(PS): production is the supply function of producer's price
QD= D(PM): consumption is the demand function of consumer's price
QO = QD: this is the market clear condition holds at the equilibrium


If we write them in percentage term:

Understanding percentage form model: we start with an equilibrium condition. When exogenous variable shocks (here is to), the linearized model tells the percentage change of endogenous variables in response.


Where η are price elasticity: % change of quantity with respect to % change of price


Note: variables in lower case are percentage change. They are not percentage change between variables but are changes before and after we alter the tax / subsidy.


Note: according to linearization of equation, if P and Q has linear relationship with no intercept: for example, PS = βQO, then the elasticity = 1.
PS = βQO
ps = qo


Note: although after shock, PM and PS do not equal their original value, but we know the change of tax rate to, which is exogenous.


Using the market clear condition: QO = QD so qo = qd, solve it as a function of parameters (η) and exogenous shock (to), we know the impact of tax on market price under new equilibrium is:
to > 0 (subsidy), ηs > 0, ηd < 0

(subsidy goes to the agent with less elasticity)


Note: this is the PE model: we focus on a certain goods' supply and demand, and solve it when price and quantity both match.


More detailed explanation of this example is available here.


Multiple commodities

If there are n commodities, the percentage change in market price would be:

Where:


Limitation of PE model


Or to summarize:


GE Example: subsidy

To solve the impact of shock with GE aspect, we need to develop a GE model (a simple one here).


Closed economy


Four agents


Two inputs


Two goods


This figure shows the flow of material in the economy (flow of monetary value is opposite)



For household, we have the utility function with two goods (food and nonfood)
Each goods have their share of consumption (CONSHR)


For food producer, we have the production function with two inputs (land and labor)


CONSHR: Share of consumption on goods


FACTSHR: factor share of factor i spent on production for good j, divided by all goods j


FACTSHR(labor, food) + FACTSHR (labor, nonfood) = 1


QFE(labor, food) = FACTSHR(labor, food) * QO(labor)


SVA: SVA(labor, food) + SVA(land, food) = 1, so I think SVA is the share of value added (share of each factor over total factor input)


To summarize:


Note: So far, we haven't set production and utility function. All equations are based on the fractional relationship of variables (forever hold)


Income formation


Before tax or subsidy:

Household income y from two primary factors


means endowment. The consumer have no incentive to set aside inputs.


Y is spent on goods:
CONSHR(food) Y is spent on food,
CONSHR(nonfood) Y is spent on nonfood.


After tax or subsidy

Y = PM(land)* QO(land) + PM(labor)*QO(labor) + net taxes


Producer

Assume constant return to scale


Input use by sector

QFE(factor, good) = FACTSHR(factor, good) * QO(factor): the quantity of factor spent on certain goods' production


Based on "Hertel, T. W. (1990). General equilibrium analysis of US agriculture: What does it contribute?. The Journal of Agricultural Economics Research, 42(3), 3-9:"


For food sector, cost share for labor and land are and , they are substitutable in food production with elasticity of substitution (Here is represented as a non-negative value)


Then the food sector's partial equilibrium supply response is


Note: this is the same as supply elasticity in partial equilibrium model.


Tax's impact on market price

Let the price of land to be numeraire, so , pm is the percentage change of market price (price for consumer)


[recall: to is subsidy for food production ps = pm + to]


So we have a vector of pm changes in the economy:



x is a shift factor, which is a function of all type model shares and elasticities


This is the special version of 4 good model solved by Keller in chapter 10.7


Note: although formulas are written in multiple lines, they are not vectors, but just one line formula.


Revise this equation

Set land price to be numeraire, and omit supply = demand for land.


Special cases of the model

If = 0 (demand is inelastic) [I suppose is the substitution elasticity between consumed goods)
or becomes infinity (supply is perfectly elastic)
Then we have: x = 0


pm(food) = -to
pm(nonfood) = 0
pm(labor) = 0
Then all price changes goes to consumer, who is inelastic (same conclusion as we get from PE model)


If = 0 (no substitution between land and labor)
or = 0 (no labor is used in food sector, or only land is used in food sector)
Then we have:

This is based on
,
Since x > 0, in this case all price go down relative to land price. Thus landowner's income rises (the income from land can now afford more expenditure since other goods' price decrease).


Implication: benefit of subsidy are shifted back to landowners.



Compare PE and GE analysis of subsidy

If we focus on the impact of subsidy on food price
And assume the food sector is small ( is close to 0, I think it means the impact on food sector has little impact on the competition of labor with nonfood sector)


In that case, PE analysis is good enough.
PE model for pm(food):
From GE model, we have:


Why we need GE analysis


When should we avoid using GE


When should use GE


Note


Example