Goods Market Equilibrium (con’t)

Investment

Determined by the level of the desired capital stock (K)

MPK is the Marginal Product of Capital = slope of the production function with all other inputs (i.e. Labour) held constant.

MPK^f is the future MPK and the expected return to investment in capital stock today.

User Cost of Capital

User Cost of Capital (uc) is the cost of owning capital. It is equal to the opportunity cost of investing in capital (i.e. the rate of return the firm could receive if they did not purchase the capital) and the depreciation of the capital stock.

uc = rp_k + dp_k = (r+d) p_k

Where        r – expected real interest rate

                   d – is the rate of depreciation

                   p_k- is the price of purchasing the capital

  Determining the level of the Desired Capital Stock (K*)

Desired Investment

The amount that must be invested today (I)  to reach the level of Desired Capital Stock tomorrow (K_t+1) is  determined by the level of Capital Stock today (K_t) and the depreciation rate:

I = K_t+1  - K_t + dK_t = K* - (1-d) K_t

By adjusting the real expected rate of interest (in the user cost function) we can map out the relationship between real interest rates and investment. This gives us a function for investment with the levels of depreciation (d) and  MPK^f held constant.

Taxes and the Desired Capital Stock

Capital is taxed at the rate т according to:

(1-   т) MPK^f= uc

Which is the equilibrium condition used to determine the Desired Level of the Capital Stock.

MPK^f= uc/(1- т) = (r+d)/(1- т)  p_k

So increases in the rate of taxation decrease the MPK^f which decreases the level of the Desired Capital Stock

Note: Taxes on capital are really applied to profits rather than on their marginal products. See Bernanke, Abel and Smith for more on efficient tax rates.

Goods Market Equilibrium

From the expenditure measure of GDP (in a closed economy) we know that:

Y = C^d + I^d + G

C^d = -S^d + Y – G

Y = I^d + G – S^d + Y – G

So in equilibrium

I^d = S^d

When the goods market is not in equilibrium (say for example S^d < I^d, such that there is less savings that firms wish to invest at that interest rate) then there is competition among borrowers (the firms) for saver’s dollars. This competition drives up the price of borrowing ( the real interest rate). If savings is greater than investment than the excess supply of funds drives down the price of borrowing and the interest rate falls.

Any factor that increases the level of desired savings, at each level of the real interest rate will cause the savings curve to shift to the right.  For example a decrease in the expected future real output will cause the savings curve to shift out as individuals expect a lower income in the future and save more.

Any factor that increases the level of desired investment (such as changes to the rate of depreciation, taxation or the MPK^f) will shift the investment curve up and to the right.

Asset Market Equilibrium

From Chapter 7 of Bernanke, Abel and Smith.

The asset market is the market in which buyers and sellers sell real financial assets.

What is money?

Money is anything that can be used as a medium of exchange between individuals who wish to engage in trade. It is a unit of account for measuring economic variables and it is a store of value so that individuals can hold onto their wealth.

Money Aggregates

Note: For more information on the money supply and money aggregates see the Bank of Canada website.

Important to understand how the supply of money in the economy is measured in 

order to fully understand how monetary policy can be used to influence it, and through it the rate of inflation.

M1 - Measures all currency in circulation and all money held in personal chequing accounts (held by individuals) and current accounts (chequing accounts held by firms). 

M2 - Everything in M1 plus personal savings accounts.

M2 + - Everything in M2 plus accounts held in other financial institutions other than banks.

M3 - Everything in M2 plus term deposits held by firms and foreign currency holdings by domestic residences.

Money Supply

The money supply is all the money available in the economy. It is influenced by the decisions of the central bank and is controlled through short term interest rates. More directly the money supply is influenced through Open Market Operations.

If the bank wishes to decrease the money supply it sells bonds to the public. The public pays for the bonds from money in circulation and the bank keeps this money out of circulation following the bond issue.

If the bank wishes to increase the money supply it buys bonds and other securities from the public in exchange for money which enters circulation.

Seignorage is when the government sells bonds directly to the central bank in exchange for newly minted currency which it uses to pay for government services (or perhaps to pay down debt). This increases the currency in circlulation.

Money Demand

Individuals allocate their wealth amongst various financial assets, including money. How they allocate this wealth, and how much money they demand is determined but the following:

Expected Return

Risk

Liquidity

No one asset offers all three of the above, usually in order to increase liquidity or decrease risk assets will offer a lower expected return. Money is the most liquid asset but offers no expected return.

How much money is demanded is part of individuals portfolio allocation decision. 

Money demand is influenced by:

Price level - The higher the price level the more money people wish to hold. Money demand is proportional to the price level, if price levels double then money demand doubles.

Real Income - The more income economies have the more transactions individuals wish to undertake. Therefore higher income generally means more money is demanded. Money demand does not necessarily increase proportionally with real income. In fact money demand grows more slowly than real income. Just how changes in income affect money demanded is determined by the  income elasticity of money demand.

Interest rates - Nominal interest rates on non-money assets (call this i) represent the opportunity cost of holding money. If money type assets (like chequing accounts) pay interest i^m then money demand is determined by the cost i - i^m. Just how interest rates affect money demanded is determined by the interest rate elasticity of money demand. 

Money Demand Function

M^d=P L(Y,i)

where M^d is the aggregate demand for money, P is the price level, Y is real income, i is the return on non-money assets. L is the money demand function. 

Dividing both sides by P gives us the demand for money in real terms.

M^d/P = L(Y,i)

Money demand is influenced by the factors noted above (including those which affect the portfolio allocation decision) and the following:

Wealth

Payment technologies

Asset Market Equilibrium

When studying the asset market equilibrium we only concern ourselves with the equilibrium condition in the market for money assets. The reason we can do this is that if the market for money assets is in equilibrium then it must be the case the the market for non-money assets is also in equilibrium.

In equilibrium the total wealth, held in money and non-money assets, demanded must equal the total wealth in the economy. The individual market for money is in equilibrium if the aggregate money demanded equals the aggregate money supplied. If this is the case than it must be true that the aggregate non-money assets demanded equals the aggregate non-money assets supplied.

Factors that affect the asset market equilibrium:

Price level -  if the price level increases the M shifts left increasing the equilibrium real interest rate.  

Expected inflation - if there is an increase in expected inflation the money demand curve shifts left and down.