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Western University

Economics

Economics 2150A/B

Peter G Brown

Winter

Description

INTRODUCTION
So far we have accomplished two things: 1) we have modeled the behavior of the
representative consumer and the representative firm and
2) we have built a labour market.
We now want to put together a model that uses what we have so far, but that also has a
government. This will be a closed economy (no foreign sector) and it will be a one period
economy. This second fact is very important because it means that borrowing and lending
can not happen in this economy since the economy only lasts for one period.
Let’s imagine what ONE PERIOD really means. It means that no market exists where
economic agents can exchange consumption over time. Now that is really confusing!!! Or
is it?
What do you do when you borrow? What you are really doing is consuming something
today and then paying for it in the future. – Example- You buy furniture today and don’t
pay for it today, but in one year’s time you pay for the furniture. Now the store will
usually charge you a fee to postpone this payment – an interest rate. (even Leon’s and the
Brick calculate the interest in the no pay until 20XX events by charging higher prices
than they would otherwise). So in effect you have borrowed from the store (the store has
lent you real consumption, in the form of furniture) and you pay the in one year. You
have really purchased two things –one is the furniture and the other is “time”. Well not
really time as time can not be purchased but the postponement of payment is measured in
time.
The cost of the borrowing and the return on lending is the interest rate.
Now getting back to our economy – these types of transactions (over two periods) can not
take place. Our model, for the moment, only lasts for one period. All agents operate
within this one period. Later we will relax this assumption and allow for borrowing and
lending, but not quite yet!
ADDIND GOVERNMENT TO THE MODEL
Remember everything in the model is measured (denominated) in terms of the
consumption good. So when we want to add government we must allow the government
to have some of the production of the consumption good to carry out their functions
This we will call government expenditure and it is the usually G in our model.
The way that the government finances this expenditure is by taking away some of the
consumption available to the consumer. This is a tax ,T, in our model. Now let’s be sure we recognize that this tax is a lump sum tax. This simply means that
the government in this simple one period model decides how much of the consumption
good it wants (G) and takes this from the production (Y) of the economy. Notice this
a“lumpsum”. The consumer is affected by this BUT the actual amount of T is simply
decided by the government-it is what is called exogenous. An exogenous variable
AFFECTS the agents in the model but is NOT DETERMINED by the agents in the
model.
Normally this is stated as follows: exogenous variables are determined OUTSIDE the
model endogenous variables are determined BY the model.
For our purposes, one way of discerning whether a variable is endogenous or not is to
look at the variable on the axes of our diagrams. If the variable appears on the x or y axis
then it is endogenous. If the variable you are considering does not appear one of the axes
then it is exogenous.
This makes intuitive sense since any point in the x,y space is a function of the two
variables. Æ endogenous.
Now given that there is only one period and that taxes are lump sum the equation that
represents the government sector is very simple indeed.
G= T
This is formally called the government’s budget constraint. It means that fiscal policy is
now in the model – fiscal policy is the expenditure (G) and tax revenue (T) of the
government.
Because the government can not borrow in the model and expenditure must be covered
by taxation during the period. Thus the budget of the government will always be
balanced-no deficit or surplus is possible. This is true because a deficit means you spend
more in one period than you have and then presumably pay for it later. – WE ONLY
HAVE ONE PERIOD-
A surplus means you have more revenue in the current period than you need and you can
spend it later – again we only have ONE period.
COMPETITIVE EQUILIBRIUM.
In this economy all agents are price takers. This means that no one agent is large enough
to affect market prices. Now in the model so far there is only one “price” and that is the real wage rate. This
means that firms and consumers face a wage rate that they both know and which clears
the labour market.
By “clears” we mean that demand equals supply.
Let pause and see what we have so far.
1). Consumer’s make decisions on leisure and consumption given the wage rate (w)Æ
this yields the labour supply curve Ns.
2). Firm’s need labour for production (to maximize profits) given w, z and KÆ this
yields the labour demand curve Nd.
3). The government decides how much of the Y it wants Æ this determines G which
determines T.
Therefore in equilibrium we have:
Ns= Nd
And G = T
Now notice what this means. Ns =Nd at an equilibrium wage rate w* and at an
equilibrium labour amount N*.
Thus this determines GDP (Y*). Remember z, and K are given.
This will also allow for the optimal amount of consumption C*.
Y* = zf(K,N*) Æ production function
Now notice that the economy must provide for the consumption of consumers and the
expenditure of the government.
Y* = C *+ G
OR C* = Y* -G
-- this is all denominated in terms of the consumption good so we say that , “the goods
market clears”. NOW for the visual representation of all this we can use a graph. The goal is to get firm’s
decision and the consumer’s decision on one graph.
Let’s look at the equations we have that will allow us to do this.
C = Y-G
But we know from before that Y = zf(K,N) and that N = h-l . Thus the production
function can be written as Y =zf(K, h-l). Use this and rewrite the consumption equation
as:
C = zf(K, h-l) –G Æ Notice the only two things that can change (variables) in this
equation are C and l. so we are back to our C,l space expect now we have a production
possibility frontier (PPF) in the diagram. The PPF is just the mirror image of the
production function; Now notice that the government expenditure G is below the origin in negative territory.
This is done simply to represent the fact that government takes away consumption goods
from the consumer. This is what is meant by the “crowding out” result of government
actions.
Now observe panel (c) above. Notice that leisure and consumption are on the x and y
axes respectively. These are the same two variables we had in the consumer’s
maximization diagram. Therefore, we can superimpose the consumer’s indifference curse
and budget constraint on to the PPF and we get out competitive equilibrium. Now let’s see what we have here. The PPF shows us how much can be produced in the
economy for different choices of leisure (work) and consumption. This also represents
what firms are producing.
Notice that the slope of the production function is just the MPN and this is what the firm
produces as it increases its labour input by successive units. These units are chosen
optimally by the consumer.
Remember the consumer choice is based upon:
MRS = w
This gives the amount of Ns supplied
Now remember that the firm chooses such that:
MPN =w
The wage rate connects these choices up!!
MPN = MRS
Now when we take the production function and put it into a diagram like panel (b) above
we just change the x axis from labour to leisure. But this is not a substantial change
because we know that when the CONSUMER chooses leisure he automatically chooses
the amount of work (h). There panel (a) and (b) are just mirror images of one another.
However by doing this exercise we have one space in leisure and consumption to put
everything into and this diagram 5.3 above.
Notice at point j all the slopes are equal. The slope of the indifference curve (MRS),
slope of the consumer’s budget constraint (w) and the slope of the PPF which we call the
marginal rate of transformation because it shows how much the ECONOMY can produce
as you give up a unit leisure for a unit of work plug this into a production function and
get output.
Thus the RATE you ca transform one good into another is the Marginal rate of
transformation (MRT). Now the best way to see the conditions that exist when there is a competitive equilibrium
is to look at the slopes of the PPF, the budget constraint and the indifference curve. AS
we have just indicated above they are all equal at point j, therefore.
MRT = w = MRS,
But we know that firm’s hire up to the point where w = MPN so:
MRT = MPN = MRS.
These are the conditions that exist when we have a competitive equilibrium. In our model
a competitive equilibrium will yield “Pareto” equilibrium as long as there are no
distorting taxes. A distorting tax is NOT a LUMP-SUM tax. A distorting tax is a tax that
that depends on the behavior of an economic agent.
For example if the government taxes wage income, then the consumer sees her wage rate
as w – tw where t is some rate of tax, say 20%.
Now wages are w(1-t) or in this example the consumer sees her wage rate as w(1-.2)
or .8w Æ in other words if the consumer sees a wage rate of 20 she knows she only gets
16 units of consumption.
However the firm still HAS TO PAY 20 units of consumption.
So now when we look at out optimal competitive equilibrium we have a distortion.
Because the consumer will set w(1-t) = MRS
But the firm sets w = MPn
Thus MRS ≠ MPn if fact MRS < MPn therefore our condition
MRS = MPn = MRT will break down.
Remember that a Pareto optimal equilibrium states that” you can not make someone
better off without making some else worse off” under conditions of perfect competition
with no externalities and no distorting taxes a

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