Equilibrium in the Flexible-Price Model

Equilibrium in the Flexible-Price Model:

Equilibrium and the Real Interest Rate:

In the flexible-price full-employment classical supposition GDP and national income Y equal potential output Y*:

Y = Y*

However the determinants of the components of real GDP are various. We saw that the exchange rate is a function of (a) the real interest rate difference between home and abroad and (b) foreign exchange traders' opinions:

ε = εo - εr x (r - rf)
     
We saw the determinants of consumption expenditure:

C = Co + Cy x (1-t) x y
     
Of investment expenditure:

I = Io - Ir x r
     
And of net exports:

NX = (Xyf x yf) + (Xs x εo) - (Xs x εr x r) + (Xs x εr x rf) - (IMy x Y)
     
Fourth as well as last we left the determination of government purchases to the political scientists:

G = G
 
These four components add up to aggregate demand or conceptually at least, total expenditure, written E when we want to emphasize that, it isn’t quite the same as real GDP Y. Nevertheless the circular flow principle guarantees that in equilibrium aggregate demand will add up to real GDP Y:

C + I + G + NX = E = Y
     
However, the determinants of each of the components of total spending E seem to have nothing at all to do with the production function that determines the level of real GDP Y. How does aggregate demand add up to potential output? Can we be sure that all the output businesses think they can sell when they hire more workers is in fact sold? The answer is that in the flexible-price full employment classical model of this section, the real interest rate r plays the key balancing role in making sure that the economy reaches and stays at equilibrium.

To understand what makes aggregate demand equal to potential output, we need to look at the market in which the interest rate functions as the price: the market for loanable funds. When you lend money the interest rate is the price you charge and the price the borrower pays. Thus we need to look at the flow of loanable funds through the financial markets, the places where household savings and other inflows into financial markets are balanced by outflows to firms seeking capital to expand their productive capacity. The equilibrium we are looking for is one in which supply equals demand in the financial markets. According to the circular flow principle if financial markets are in equilibrium then the sum of all the components of spending is equal to real GDP.

If supply equals demand in the flow-of-funds through financial markets then aggregate supply (real GDP, Y, equal to potential output Y*) is equal to aggregate demand (the sum of all the components of total spending: C+I+G+NX). To see this, begin by assuming that real GDP is equal to potential output Y* and that the circular flow principle holds: real GDP is equal to aggregate demand:

Y* = Y = C + I + G + NX

Then rewrite this expression by moving everything except for investment spending I over to the left-hand side.

Y* - C - G - NX = I

Now comprise taxes T in the left-hand side:

(Y* - C - T) + (T - G) - NX = I
     
Note that the right-hand side is merely investment the net flow of purchasing power out of the financial markets as firms increase money to build factories and structures and boost their productive capacity. The left-hand side is equivalent to total savings: the flow of buying power into financial markets as the government, households and foreigners seek to save by committing their money to buy precious financial assets here at home. Therefore we see that whenever the circular flow principle holds the supply and demand in the flow of money through financial markets balances as well.

The (Y*-C-T) inside the initial set of parentheses are households' savings. For the reason that national income is equal to potential output, Y* is merely total household income. Subtract taxes, Take income, subtract consumption spending and what is left is household savings: the flow of buying power from households into the financial markets.

The (T-G) inside the subsequent set of parentheses are just government savings: the government's budget excess (or the government’s budget deficit, government dissaving, if G happens to be larger than T). They are the flow of money from the government into the financial markets.

Minus Net Exports Equals the Capital Inflow
:

210_capital inflow.jpg

The final term--minus net exports -NX--is the net flow of purchasing power that foreigners channel into domestic financial markets. If net exports are less than zero foreigners have some dollars left over. They then have to do a little with these extra dollars. Foreigners find dollars valuable in only two ways. First, they are of use for buying our exports (however if net exports are less than zero there aren’t enough exports to soak up all the dollars they earn). Second, dollars are helpful for besides buying stocks, buildings, property here--land, bonds. Therefore this last term is the net flow of purchasing power into domestic financial markets by foreigners wishing to park a few of their savings here. (moreover when net exports are positive, this term is the net amount of domestic savings diverted into overseas financial markets).

What happens if the flow-of-funds doesn’t balance--if at the current long-term real interest rate r the flow of savings into the financial markets surpasses the demand by corporations and others for purchasing power to finance investments? If the left-hand side is exceeding the right, a few financial institutions-- mutual funds, banks, venture capitalists, insurance companies, whatever--will discover purchasing power piling up as more money flows into their accounts than they can find good securities as well as other investment vehicles to commit it to. They will try to underbid their contenders for the privilege of lending money or buying equity in some particular set of investment projects. How do they underbid? They underbid by saying that they would admit a lower interest rate than the market interest rate r. Therefore if the flow of savings exceeds investment the interest rate r falls. As the interest rate r fell the number as well as value of investment projects firms and entrepreneurs found it worthwhile to undertake rises.

Excess Supply of Savings in the Flow-of-Funds Market:

1012_flow of fund market.jpg

Legend: When the interest rate is such that there is an surplus supply of savings:

Some savers are about to propose to accept a lower interest rate and the interest rate is  about to drop.

The process will discontinue when the interest rate r adjusts to bring about equilibrium in the loan able funds market. The flow of investments into the financial markets will then be just equal to the flow of purchasing power out of financial markets, as well as into the hands of firms and entrepreneurs using it to finance investment.

Solving the Model:

At what stage of the real interest rate will the flow-of-funds through financial markets in equilibrium?

First let’s look at the determinants of the provider of private savings:

Y* - C - T = (1 - t - (1-t) Cy) Y* - Co

Second let’s seem at the determinants of public savings:

T - G = tY* - G bar

Third let’s seem at the determinants of international savings:

- NX = IMyY + Xεεrr - XyfYf - Xεεo - Xεεrrf
     
These three added mutually make up the flow-of-funds supply of savings. The flow-of-funds demand for savings is merely the investment function:

I = Io - Irr

Equilibrium is, obviously where the supply of savings is equal to investment demand. To get an unambiguous expression for the interest rate, start by writing out the determinants of all the pieces of savings:

2296_determinant of savings.jpg

Grouping all the terms that depend on Y* on the left of the left-hand side all the terms that depend on international factors on the right of the left-hand side, all the terms that are constant in the middle of the left –hand side, and move all the terms with the real interest rate r over to the right-hand side:

106_determinant of savings_1.jpg

Moreover divide by -(Ir + Xεεr) to determine the equilibrium real interest rate r:

 

278_determinant of savings_2.jpg

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