THE SHORT RUN FIXED PRICE ANALYSIS OF THE PRODUCT MARKET

We now turn to the derivation of aggregate demand under fixed price of final goods and constant rate of interest in the economy. In order to hold price constant at any particular level, however, one must assume that the suppliers are willing to supply whatever amount consumers will demand at that price. If quantity supplied is either in excess of or falls short of quantity demanded at this price, price will change because of excess supply or demand. To avoid this problem, we assume that the elasticity of supply is infinite – i.e., supply schedule is horizontal – at the fixed price. Under such circumstances, equilibrium output will be solely determined by the aggregate amount of demand at this price in the economy. We call it effective demand principle. Note also the word short run. We assume that prices in the economy take some time to respond to the forces of excess supply or demand. In the mean time, producers try to update their production plans in order to avoid excess supply or demand. For instance, if they face an excess supply in the current production cycle they will plan to produce less in the next cycle so as to avoid accumulation of stocks in their warehouses. Note also that an individual producer is very small compared to the size of the national market and, therefore, she cannot affect market price on her own. An individual producer has to accept the price that prevails in the market. The aggregate price level in the economy changes only when adjustments in all markets of the economy fail to eliminate the excess demand or supply. Prices are, therefore, assumed to vary only in the long run.

A Point on the Aggregate Demand Curve

At a fixed price, the value of ex ante aggregate demand for final goods, AD, is equal to the sum total of ex ante consumption expenditure and ex ante investment expenditure. Under the effective demand principle, the equilibrium output of the final goods is equal to ex ante aggregate demand, as represented by equation 4.3

Y = A + c.Y

where A is the total value of autonomous expenditure in the economy. Let us consider a numerical example to derive the value of the aggregate demand and hence equilibrium output in the economy at a fixed price. Suppose the values of the autonomous expenditures are C = 40, I = 10 and the value of mpc, c = 0.8. What will be the equilibrium value of Y ? Consider Y = 200, as a trial solution. At this output, the value of the ex ante consumption expenditure is C = C + 0.8.Y = 40 + (0.8)200 = 200, ex ante investment expenditure is I = I = 10 and ex ante aggregate demand is AD = C + I = 200 + 10 = 210. At the level of output Y = 200 the value of ex ante aggregate demand is 210, which denotes a situation of excess demand. Clearly, Y = 200 is not the equilibrium level of output in the economy. Consider, next, the output level Y = 300. Calculations similar to the above case shows that the value of ex ante aggregate demand will be

A + cY = C + I + cY = 50 + (0.8)300 = 290.

The ex ante aggregate demand falls short of the output and there is excess supply. Hence, Y = 300 is also not the equilibrium level of output in the economy. Finally, consider Y = 250. At this output, AD = 50 + (0.8)250 = 250. We have ultimately hit the correct value of Y, at which aggregate demand equals aggregate supply. Y = 250 is, therefore, the equilibrium output of the economy at the fixed price-interest rate combination.

Effects of an Autonomous Change on Equilibrium Demand in the Product Market

What are the determinants of the equilibrium value of aggregate demand at fixed price? In other words, what governs whether the equilibrium aggregate demand would be 250 or 210 or 290 in the above example? The equilibrium output and aggregate demand at the fixed price-interest rate is derived by solving the equation Y = AD = A + cY . It is an equation involving only one variable, Y . The solution of the equation is

Y = 1– A c (4.4)

The value of Y will, therefore, depend on the values of the parameters on the right hand side, which are A and c in this case. In the above example, the equilibrium value of aggregate demand, 250, and hence the position of the single point on the aggregate demand schedule that we have derived so far, will depend on the values of these parameters. Compare the equation AD = A + cY with the equation of a straight line of the standard form: b = å + ma, as discussed in section 4.2. A is the intercept parameter and c is the slope parameter of this equation. When c increases, the straight line representing the equation of aggregate demand will swing upwards. On the other hand, as A increases, the straight line will shift in parallel upwards. However, A is only a composite term, representing the sum of C and I , which are, therefore, the truly shifted parameters of the AD line. Suppose I increases from 10 to 20. What will happen to equilibrium output and aggregate demand?
The Multiplier Mechanism

Clearly, 250 is no longer the equilibrium value of output or aggregate demand. With I = 20, aggregate demand in the economy will be equal to 40 + 20 + (0.8) 250 = 260 from equation (4.4), which is greater than the output Y = 250 by the amount of the increment in the autonomous investment (Ä I = 10). There is excess demand in the economy and producers will have to run down their inventory to meet this extra demand. Thus, in the next production cycle, they revise their production plan upwards, i.e. increase the value of their planned supply of output by 10 to restore equilibrium in the final goods market. In the absence of a government imposing indirect taxes or disbursing subsidies, the value of the total output of final goods or GDP is equal to National Income. The production of final goods employs factors such as labour, capital, land and entrepreneurship. In the absence of indirect taxes or subsidies, the total value of the final goods output is disbursed among different factors of production – wages to labour, interest to capital, rent to land etc. Whatever is left over is appropriated by the entrepreneur and is called profit. Thus the sum total of aggregate factor payments in the economy, National Income, is equal to the aggregate value of the output of final goods, GDP. In the above example the value of the extra output, 10, is distributed among various factors as factor payments and hence the income of the economy goes up by 10. When income increases by 10, consumption expenditure goes up by (0.8)10, since people spend 0.8 (= mpc) fraction of their additional income on consumption. Hence, in the next round, aggregate demand in the economy goes up by (0.8)10 and there again emerges an excess demand equal to (0.8)10. Therefore, in the next production cycle, producers increase their planned output further by (0.8)10 to restore equilibrium. When this extra output is distributed among factors, the income of the economy goes up by (0.8)10 and consumption demand increases further by (0.8)210, once again creating excess demand of the same amount. This process goes on, round after round, with producers increasing their output to clear the excess demand in each round and consumers spending a part of their additional income from this extra production on consumption items – thereby creating further excess demand in the next round.

We shall conclude the fixed price-interest rate analysis of the final goods market with an interesting counter-intuitive fact – or a ‘paradox’. If all the people of the economy increase the proportion of income they save (i.e. if the mps of the economy increases) the total value of savings in the economy will not increase – it will either decline or remain unchanged. This result is known as the Paradox of Thrift – which states that as people become more thrifty they end up saving less or same as before. This result, though sounds apparently impossible, is actually a simple application of the model we have learnt. Let us continue with the example. Suppose at the initial equilibrium of Y = 250, there is an exogenous or autonomous shift in peoples’ expenditure pattern – they suddenly become more thrifty. This may happen due to a new information regarding an imminent war or some other impending disaster, which makes people more circumspect and conservative about their expenditures. Hence the mps of the economy increases, or, alternatively, the mpc decreases from 0.8 to 0.5. In aggregate demand, AD = A + cY , by an amount equal to (0.8 – 0.5) 250 = 75. This can be regarded as an autonomous reduction in consumption expenditure, to the extent that the change in mpc is occurring from some exogenous cause and is not a consequence of changes in the variables of the model. But as aggregate demand decreases by 75, it falls short of the output Y * 1 = 250 and there emerges an excess supply equal to 75 in the economy. Stocks are piling up in warehouses and producers decide to cut the value of production by 75 in the next round to restore equilibrium in the market. But that would mean a reduction in factor payments in the next round and hence a reduction in income by 75. As income decreases people reduce consumption proportionately but, this time, according to the new value of mpc which is 0.5. Consumption expenditure, and hence aggregate demand, decreases by (0.5)75, which creates again an excess supply in the market. In the next round, therefore, producers reduce output further by (0.5)75. Income of the people decreases accordingly and consumption expenditure and aggregate demand goes down again by (0.5)2 75. The process goes on. However, as can be inferred from the dwindling values of the successive round effects, the process is convergent. What is the total decrease in the value of output and aggregate demand?