Notes on the Classical Market Clearing Model

The economy in the long run: Classical Market clearing Model

The Economy in the long run Assumptions

• The productive Capacity of the economy is fixed
• The time frame of the long run model, 10-15 years, is short enough that the capital stock is not growing quickly enough to increase full-employment output
• The Aggregate supply curve is vertical (Classical aggregate supply curve)

 

3.1 The supply of goods and services: The production function and the labor market

 

Production Function: The production function is a technological relationship showing how much output can be produced for a given combination of inputs.

• (Y) or output is assumed to be produced through a production function, which combines factors of production (K), and labor (N)
• The basic production form: Y= AF(K, N)
• The term (A) accounts for the level of technology or productivity

 

Cobb-Douglas production function: Y=AKO N1-0

• 0 and 1-0 are weights equal to capital’s share of income and labor’s share of income (fraction of total output that compensates each function)
• Canada’s production function is Y= AK0.3 NO.7
• Ideally a measure of A helps economists understand the functions of the economy
• A= Y/ K,N (Solow residual). However, A can change if the units the other variables are measured in change. This problem can be overcome how total factor productivity has changed over the years
• Measured this way we can see that A (factor productivity) decreases during economic slowdowns and increases during recoveries

Long run assumptions of production function

• Abstract from productivity changes and A can be ignored
• Changes in the capital stock are small enough that their effect on full-employment output can be ignored.
• Y= F(K,N)
• For a given technology and capital stock, the amount of output depends on the amount of labor input.
• The Cobb-Douglas production function can be used to graph the production function of the economy
• Capital and technology become fixed at their 2002 levels ( Y= 18.7* (949.9 o.3) No.7 )
• The production function relates the amount of output that can be produced using various amounts of labor input, holding capital and technology constant.
• The production function is used to derive the demand for labor curve.

 

The production with fixed capital and technology. Fig. 3.1 p. 52

 

• Positive slope: when a unit of technology is added to production process, even though technology and capital are fixed, output goes up.
• Marginal Product of Labor (MPN): shows the amount of output, which increases for each additional unit increase. The slope of the production function gives the MPN.
• Diminishing marginal product of labor: shows that as labor increases, the amount of extra output that is gained from an increase in labor input becomes smaller.
• The marginal product of labor: is downward sloping, as each additional until of labor contributes less to output than the previous unit did.

Marginal Product of Labor and Demand. Fig 3.2 p. 53

 

• The goal of any profit maximizing firm is to maximize profit, which equals total revenue minus total cost.
• When a firms hires an additional unit of labor, it incurs a marginal cost and receives a marginal benefit.
• The marginal benefit to a firm is the value of the additional unit of output that is produced by that additional unit of labor is called the value of the marginal product. It is measured as the marginal product (MPN) x the price;

W= MNP X P

• The profit maximizing condition is represented by the real wage. Real wage is defined by the payment to labor measured in terms of output, calculated as the nominal wage divided by the price level; w= W/P or
• A profit maximizing firm will hire labor until the real wage equals the marginal product of labor w= MPN.
• The demand for labor curve is simple the MNP curve drawn with real wage on the y-axis.

The Supply for Labor. Fig 3.4 p. 55

 

• We assume that workers, in deciding how much labor to supply, compare the costs and benefits of working an extra hour.
• The marginal benefit of working an extra hour is measured by how much this extra hour of work will increase consumption.
• When a person works an extra hour he or she receives a nominal wage
• Given this nominal wage the amount of extra consumption that can be made depends on the price of goods and services, measured by price level (P)
• The ratio of W to P is W/P, is the real wage and measured in terms of goods and services
• In this manner the benefit of working an extra hour is measured by the real wage, w.
• The marginal cost of working an extra hour is the hour that worker must give up other non-work activities. This is called leisure.
• Therefore, workers supply labor up to the point where marginal benefit equals marginal cost.
• We assume that increases in the real wage make it more attractive to give up an extra hour of leisure, therefore the labor supply curve slopes upward.

 

Equilibrium in the Labor Market

 

Full employment: occurs when all members of the labor force are employed; individuals not working are not counted in the labor force and therefore are not counted as being unemployed.

• The intersection of point (N, w) represents equilibrium in the market
• In the classical model all prices are assumed to be flexible, which ensures that the markets are in equilibrium at all times.
• In the labor market real wage is assumed to be moving very quickly, therefore equilibrium (N) is at the full employment of labor workforce.
• At equilibrium all workers in the labor force are employed.
• Any individuals who are not working are not in the labor force because the real wage is too low for them to seek employment are choosing not to enter the workforce therefore cannot be counted toward unemployment.

 

To determine output at this level the equation is

 

Y*= F(K,N*)

 

Capital and Technology are fixed;

Y* is the level of output the economy would reach if all prices were flexible and all factors of production were fully employed but not growing

 

The Classical Aggregate Supply Curve

The Classical Aggregate Supply curve is vertical because in the long run the supply of goods and services depends only on the production function. Y, depends only on N (for a given fixed level of capital and technology). Also in the labor market N depends upon the real wage, (w). Therefore, the production, or supply, in the long run is independent of the price level.

 

3. 2 The Demand for Goods and Services

Underlying Assumptions

• The Demand for goods and services is made up of C+I+G+NX.
• In the long run, government spending is exogenous.
• The long run model is interested in consumption and savings decisions of households and investment decisions of businesses.

 

Introduction

 

• The focus is on aggregate demand, which explains how income is allocated among the different spending units C + I + G + NX
• Growth theory is an important question of how a consumer allocates current income between consumption today and consumption in the future
• A decision of consumers to spend less today is really a decision to consume more tomorrow
• In an economy savings by consumers feeds into investment by firms, and investment is an increase in the capital stock

 

Consumption and Savings

 

• We can apply the same fundamentals of weighing the costs and benefits to the framework of consumption and savings as we did with worker’s desire to work more hours.
• When an individual receives income, he or she must allocate it between current consumption and savings
• The rate of time preference is the rate at which individuals are willing to give up consumption today to be compensated by increased consumption in the future;

1.     If you are inclined to be a saver you will have a low rate of time preference

2.     If you are inclined to spend you perceive a large cost to giving up current consumption and will have a high rate of time preference

3. Giving up current consumption in savings is thus impacted by the marginal benefit of savings given by the real rate of interest

4.     As real interests rates increase consumers desire to save more, shown by an upward sloping curve

5.     The curve is drawn in a Private savings curve (Sp) to distinguish the function from government savings

 

Investments

 

• Firms purchase machinery and equipment to increase their productive capacity in terms of capital stock
• Investment demand depends on the real rate of interest

 

Example

How does a firm know whether borrowing money is profitable?

 

A 1 million dollar expansion is expected to generate an extra 100,000 dollars in revenue for the firm. The firm will be willing to borrow money if the cost of borrowing is lower or equal to the return or benefit.

 

(1 million/100,000) gives the rate at which firms will be willing to borrow. At 10% interest rates or lower the firm in this scenario will borrow money to finance an expansion.

 

• Thus, investment spending is negatively related to the real rate of interest and the investment demand curve slopes downward

 

Equilibrium: Savings Equals Investments

 

• In the classical model, the Aggregate Demand is concerned with the allocation of income
• When consumers save, they can be though of as lenders, or suppliers of funds
• Businesses (when they are making decisions to borrow for expansion are investing). Businesses can be though of as demanders of funds
• There is equilibrium when lenders supply the amount borrowers demand. Therefore, equilibrium exists when savings = investments

 

Algebraic equations

 

National Account Identity for closed economy	Y = C + I + G
What are investments?	I = Y – C – G
Disposable income	YD = Y + TR – TA
Disposable income and National identity	(YD-C) + (TA- TR- G)= I     S = Sp + Sg = I
Government Surplus or Deficit *Also government savings (Sg)	TA- TR- G
Private savings (Sp)	YD-C

 

FISCAL POLICY AND SAVINGS

 

• Effects on equilibrium:

1.     When total savings decreases, the savings curve shifts to the left

2.     When total savings increase, the savings curve shifts to the right

• An increase in government purchases reduces government savings (TA-TR-G). The curve shifts to the left and on the graph shows a higher real interest rate and lower savings and investments.
• Thus we can conclude that a government budget deficit lowers savings and increases interest

 

3.3 The Money Stock, the Price level, and the Inflation rate

 

Assumptions

 

• There is a close relationship between money and the price level
• In the long run the rate of inflation in an economy is determined by the rate of growth of nominal money

 

Money

 

The major function of money is as a medium of exchange. This is summarized through the quantity theory of money equation:

 

MV= PT

Where T represents all the real transactions in the economy over a period of time and where P represents the average price of all these transactions. M is the size of the money stock (supply) and V is the velocity of circulation, which is a measure of the speed with which money circulates in an economy.

 

V= PT/M

 

In reality it is difficult to measure T. Therefore a proxy for T exists. We use Y the measure for real GDP as a substitute for in the equation.

 

MV= PY

 

• PY is a measure of the dollar value of the transactions in an economy, which is just nominal GDP.

Money Market

• We assume that there exists a money market with money supply and money demand.
• When individuals demand money, they do so in order to purchase goods.
• Money is a nominal variable. We express nominal money in terms of the number of goods it can purchase as M/P which is the real money stock.
• The demand for money equation is expressed as

 

Md/P= kY