income determination the monetary dimension - ii
TRANSCRIPT
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Income DeterminationThe Monetary Dimension - II
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Overview$ Keynesian Income Determination Models
Private sector Consumption demand Investment Demand
Supply & demand for money Public Sector
Government expenditure Government taxes Monetary policy manipulation of money supply
International imports, exports, net exports
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Money Demand
$ In Classical economics we saw an analysis of the supply and demand for "loanable funds" supply = deposits in banks of money being saved demand = borrowing from banks deposits, mostly for
investment
$ In Keynesian analysis focus shifts to demand for money, to those who want to hold money, as opposed to interest bearing assets and their reasons
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Keynes gave three motives
$ Transactions demand$ Precautionary demand$ Speculative demand
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Cost of holding money
$ Money vs C&F's "bond"$ If you hold cash, you earn no interest
income$ If you hold an interest bearing account
you do earn interest$ So, assuming profit maximizing behavior,
you would expect people to deposit all their money into interest bearing assets unless they had reasons to do otherwise
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Transaction Demand$ Main reason to hold money: to have it on
hand to finance various transactions you keep money in your pocket to by a coke you keep money in your checking acct to pay rent businesses keep money for regular purchases
$ Income and transaction demand income and spending are not synchronized e.g., income comes in once a month e.g., money needs to be spent more frequently
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Optimal Balance
$ On the one hand you want to earn interest$ On the other you need money in hand$ How much?
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Transactions Demand Graph$ One way to think about the transactions
demand is in relation to income: md = kY, the more income, the more cash needed
Y
md
mdt = kY
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But you can also earn i
$ So there is a trade-off$ Amount to be held for transactions
determined by interest rates vs transactions costs, i.e, how much it costs you to convert interest bearing assets to money
$ Given costs, the higher the interest rate, the less money you would want to hold
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Transactions Demand for Money
$ Lower the interest rate, greater the demand for money
Mdt
Money, M
interest rate i
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Precautionary Demand
$ People hold money because they can't anticipate every need, there is uncertainty, so they hold more
$ With uncertainty independent of the interest rate then you might expect the Md curve to be a little more to the right than otherwise.
$ "IF" the interest rate measures risk, then the Md curve might be steeper
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Precautionary Demand Graph$ One way to think about the precautionary
demand is in relation to income: mdp = jY, the more income, the more cash might be needed
Y
md
mdp = jY
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Speculative Demand
$ Speculation = buying an asset in the hopes that its price will rise, e.g, a bond
$ bond prices vary inversely with interest rates, i.e., if interest rates rise, bond prices fall and visa versa
$ So, the lower interest rates, the more you might expect them to rise and bond prices to fall, so you would hold fewer bonds and more money, so shape is same
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Speculative Demand$ Speculative Demand, a lot like transactions
demand
Mds
M
i
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Total Demand for Money$ Transactions (Mdt) + Precautionary (Mdp) +
Speculative (Mds)
Md, LPC
Liquidity Preference Curve
M
i
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Quantitative Considerations
$ The demand will vary according to income, Keynes was concerned with this prices, Keynes largely ignored this (we will too)
$ A rise in income will shift curve to right$ A rise in the price level will shift curve to
right$ So Md = f(i, Y, P)$ With dMd/di < 0, dMd/dY > 0, dMd/p > 0)
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Equilibrium Interest Rate
$ Combine demand with supply of money
Md, LPC
Ms controlled by FedINTEREST
M
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Fed Policy - I
$ Expand supply of money to decrease i
Md, LPC
Ms controlled by Fedi
M
Msi
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Fed Policy - II
$ Contract supply of money to increase i
Md, LPC
Ms controlled by Fed
Msi
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Link Money w/Income Determination Model
$ Y = C + I + G + (X - M)$ C = a + bY$ I = e + fY$ Md = f(i, Y, P)$ Ms = Ms
$ Where is link? Between i & I, i & C (Keynes only concerned with link btwn i & I)
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Marginal Efficiency of Capital
$ Amount of investment is determined by comparing expected rate of return to i
Investment
i
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Marginal Efficiency of Capital
$ Amount of investment is determined by comparing expected rate of return to i
Investment
i
MEC
higher the interest rate, the less theinvestment forthcoming
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Fed Policy & Investment
$ Keynes focused on Fed influence on I thru manipulation of i
I
LPC MEC
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Money Policy & Income
$ If Ms iI$ then with Y = C + I + G + (X - M),$ an I Y$ which we can see in the following 3 part
diagram
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MECLPC
Investment, Savings
INCOME
INTEREST
Y
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Feedback Effect$ However, remembering that$ Md = f(i, Y, P), dMd/dY > 0$ We know that an increase in Y will result
in a right shift in Md, offsetting the increase in Ms somewhat so i won't be quite as low, and thus also I & Y won't increase as much
$ Two solutions: algebraic change models
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IS - LM Model
$ Alternative formulation of Keynesian model which moves consumption to background and highlights interest rate.
$ IS = locus of equilibrium points between investment and supply (I & S, IS)
$ LM = locus of equilibrium points in supply & demand for money.
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IS - LM Graph
LM
IS
INTEREST
YYe
ie
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Ms
LM
IS
INTEREST
YYe
ie
Y'e
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Derivation of IS
$ We begin with the MEC shedule which we will assume is linear, I = e + fY + gi
MEC
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Derivation of IS
$ From this we know what I will be generated by any given level of I
MEC
Investment
i
i1
I1
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Algebraic
$ If our linear MEC curve is given by the equation I = e +gi, [or i = e + gI] w/g<0 NB: given our past discussion of investment we would
be more likely to use I = e + fY +gi. This would cause no problem in solving the model for equilibrium Y, but in this simple graphic derivation we leave Y out because it is Y we are looking for.)
$ Then for any given i we can calculate the level of investment, I that we would expect to be forthcoming at that I.
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I = S$ We also know that in equilibrium I = S, so
if we know I1 we also know what S1 will be
Investment
Savings
I1
S1
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S = -a + (1 - b) Y
$ But from the savings function, we know the level of Y necessary to generate S1
S1
Y1
Y
Savings
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Algebraic
$ Given a rate of interest (i), we found the resulting level of investment (I)
$ We know that in equilibrium, I = S$ Therefore, we know S$ The only question that remains is what
level of Y will generate that level of S$ We can find this from the Savings function
(S = -a + (1-b)Y)
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Equilibrium Point
$ So, beginning with a given interest rate, we have found the level of Y at which I = S.
$ We can repeat this procedure to obtain the locus of points that forms the IS curve.
$ We can also put these four diagrams together to see their interaction
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MEC
S
Investment
Investment
i
i
Savings
Income
i
i1
I1
S1
Y1
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MEC
S
Investment
Investment
i
i
Savings
Income
i
i1
I1
S1
Y1
i2
I2
S2
Y2
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MEC
S
Investment
Investment
i
i
Savings
Income
i
i1
I1
S1
Y1
i2
I2
S2
Y2
IS
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Algebraic
$ If Y = C + I$ and if C = a + bY, I = e + fY + gi$ then, Y = a + bY + e + fY + gi$ Y - by - fY = a + e + gi$ Y(1-b-f) = a + e + gi$ Y = a/(1-b-f) + e/ (1-b-f) + [g/ (1-b-f)]i
-- an equation in Y and i of the sort Y = f(i) [or we could find i = f(Y)] which is what we are looking for.
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Derivation of LM$ We begin with the speculative demand for money,
assuming some i, we know the level of Mds that will be desired
Mds
Speculative demandms = L(i)
M
i
i1
Md1
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Algebraic
$ In linear form, the relation between the interest rate and the speculative demand of money is of the sort:
$ i = m + nMds where n<0, e.g.,: $ i = 5.1 - 0.05Mds
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Total M = Mdt + Mdp + Mds
$ So, total M can be divided btwn Mds and Mdt + Mdp (which we will lump together)
Mds
Mdt + Mdp
Md1
and derive how much money will beheld for transactions and precautionary motives
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Algebraic
$ The total demand for money,
$ M = Mdt + Mdp + Mds
$ in equilibrium, will be equal to the supply and therefore given (M)
$ so if we have found Mds, then Mdt + Mdp will = M - Mds
$ and both Mdt and Mdp are determined by Y, therefore we can find the level of Y that will generate Mdt + Mdp
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Mdt + Mdp
$ We can combine the Mdt and Mdp curves as both are a function of Y and ask what level of Y will generate Mdt + Mdp
Mdt + Mdp
Y
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One Point on LM
$ We now have a level of Y that will be compatible with the originally posited level of interest. That level of Y will generate a level of transactions and precautionary demand compatible with the desired level of speculative demand.
$ We can see the relationships in the following diagram.
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Mds
Mdt
+Mdp
Mdt
+Mdp
MY
i i
Mds
Y
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Mds
Mdt
+Mdp
Mdt
+Mdp
MY
i i
Mds
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Mds
Mdt
+Mdp
Mdt
+Mdp
MY
i i
MdsLM
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Algebraic - I
$ i = m + nMds where n<0$ Mds = i/n - m/n$ M = Mds + [Mdt + Mdp]$ [Mdt + Mdp] = Mdy = f(Y), say $ Mdy = p + qY$ M = i/n - m/n + p + qY, but Md = Ms, so for
every Ms,$ we can find an equation in Y and i
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Algebraic - II
$ In problems all this is sometimes simplified into a single demand for money function, e.g.,
$ i = 5.1 - 0.05Md$ ignoring the dependence of Mdt and Mdp
on Y, e.g., sample test #2 on web-forum
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Thus, the IS - LM Graph
LM
IS
INTEREST
YYe
ie
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Algebraic
$ Each of these two curves are represented mathematically as equations of the sort: i = r + sY
$ Therefore, an equilibrium solution can be found by solving the two equations simultaneously for i and Y.
$ You now have two ways of solving these models simply combine all the equations and givens find the equations for IS and LM curves and solve
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Fiscal Policy & IS Curve
LM
IS
INTEREST
YYe
ie
IS'
Y'e
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Monetary Policy &LM
LM
IS
INTEREST
YYe
ie
LM'
Y'e
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Homework
$ Now, factor in G and T and re-derive the IS and LM curves. How does their inclusion change the graphs?
$ Finally, factor in net exports (X - M) and do the same.
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