This post is a continuation of my previous post Market Structure: Classical Vs. Keynesian Assumption (Give it a quick read to gain context).
The Classical macroeconomic model assumes that markets (Output as well as Factor markets) are Perfectly Competitive. Perfectly competitive markets tend to operate at the 'Full Employment' level. In this post, we'll demonstrate why, by explaining how Price and Output are determined in Perfectly competitive markets.
How Price and Output are determined in a Perfectly Competitive Output Market
1. In a perfectly competitive Output market, the price (P0) of a product is determined at the intersection of the Market demand and Market supply curves (see chart 1: Output market). While market demand depends on consumer preferences, the market supply curve is simply an aggregation of the supply curves of the individual firms comprising the output market.
Chart 1: Determination of Price and Output (top panel), as well as Wage and Labour Employed (lower panel) in Perfectly Competitive Markets
2. How do we get the Supply curve for an individual firm?
Since each individual firm wants to maximize profits, it will sell up to the point where its Marginal Revenue (MR) (revenue from the sale of an incremental unit of output) is = its Marginal Cost (MC) (cost of producing an incremental unit of output). The MR for a competitive firm = the Price of its output. Hence, the supply curve for this firm is simply its MC curve (See chart 1: Firm output).
3. How do we derive the Demand curve for an individual firm?
The price of the firm’s output (P0) is determined by the intersection of the market demand and market supply curves, as we noted above. This price (P0) is taken as a ‘given’ by all the firms comprising the market because each of these firms is too small to impact P0 in any way. Hence, the demand curve for each of these firms is perfectly elastic (i.e. flat) at price P0, meaning that they can sell any amount of output that they produce at this market-determined price (See chart 1: Firm output).
4. How much does each firm produce?
Each firm produces upto the point where the demand for its output = the supply of its output i.e. P0 = MC. You can see in the chart above (Firm output) that each firm will produce an output “x0” at price P0.
Overall, the Output market will produce X0 quantity of output (summation of the output of all the individual firms or Σx0) at price P0.
How Wage and Labour Employed are determined in a Perfectly Competitive Labour Market (i.e. the market where the firms operating in our Perfectly Competitive Output market buy their labour)
So far, we’ve discussed how price and output quantity are determined in a Perfectly competitive Output market. Where do the firms operating in this Output market buy their labour? Per Classical economic theory, from a perfectly competitive labour market. Let's now demonstrate how Wage and Labour Employed are determined in this labour market.
1. How is Wage determined in the Labour market?
The Classical model assumes that all markets are perfectly competitive including the labour market. Consequently, equilibrium wage (w0) is determined at the intersection of labour market demand and labour market supply curves (See chart 1: Labour market). The labour market demand curve is nothing but the aggregation of the labour demand curves of individual firms in the output market.
2. How do we derive the Labour Demand curve for an individual firm?
As discussed above, each profit maximizing, competitive firm produces output upto to the point where P0 = MC. From this condition, I’m going to derive the labour demand curve of this firm. Here goes:
MC = ΔFC/ΔQ + ΔVC/ΔQ where FC = fixed cost, VC = variable cost
What this means is that MC = increase in FC due to the production of an incremental unit of output + increase in VC due to the production of an incremental unit of output.
Since FC is constant and does not change with the number of units of output, ΔFC/ΔQ = 0; MC is simply = ΔVC/ΔQ. We further assume that the only VC of production is the labour cost.
Hence, MC = w * ΔL/ΔQ (1)
where w = wage, ΔL = change in amount of labour employed, ΔQ = change in output
Let us now define a new term, the Marginal Product of labour (MPL). It is = the units of output produced by employing an additional unit of labour, keeping everything else constant.
So, MPL = ΔQ/ΔL (2)
Substituting (2) in (1)
MC = w/MPL (3)
But remember, the firm produces output till MC = P0.
Substituting this in (3) gives us the firm’s labour demand curve:
P0 = w/MPL or
w = P0 * MPL
At any wage (w), the firm demands labour upto the point where the price of its output (P0) multiplied by the Marginal Product of the last unit of labour employed (MPL) is = w (see chart 1: Firm labour demand).
To hire labour, the firm will have to pay the equilibrium wage = w0, determined by the market demand and market supply for labour. Each firm will take this wage (w0) as given since it’s too small to affect the wage rate. Hence, the labour supply curve for each firm will be perfectly elastic (flat) at wage = w0. The firm can employ any amount of labour by paying a wage of w0. See chart (Firm labour demand).
4. How much labour does each firm employ?
Each firm will employ labour upto the point where its demand for labour is = the supply of labour available to it i.e. till w0 = P0 * MPL.
You can see in the chart above (Firm labour demand) that each firm will demand “l0” quantity of labour at wage w0. Overall, L0 units of labour (summation of the labour employed by all individual firms or Σl0) will be employed in the labour market at wage w0.
Conclusion: when Output and Labour markets are Perfectly Competitive (as assumed in the Classical model), they tend to operate at the 'Full Employment' level
To appreciate what this means, let’s remind ourselves of the meaning of “full employment”. Full employment refers to the situation in the labour market, where at the existing wage, everyone who wants to work is able to find work i.e. market demand for labour is = market supply for labour. This is the case in Chart 1 (Labour market) where at w0, the demand for labour (DL) is = the supply for labour (SL).
This is always the case for perfectly competitive markets. As we’ve explained above, the existing wage in a perfectly competitive labour market is always determined at a point where labour demand = labour supply. Further, this demand for labour is derived from firms operating in a perfectly competitive output market where price and quantity are again determined at a point where market demand for the output = market supply.
Bottom-line, general equilibrium (when all interacting markets in an economy are in equilibrium) in perfectly competitive markets is always at the 'full employment' level - else prices adjust (rise/fall) to make it so.
This is what the Classical model of economic theory assumes. The Keynesian model on the other hand, rejects this assertion. To understand what the Keynesian model says about market structure and Full employment, read my next post Why do Real-World Markets Not Tend to Operate at the 'Full Employment' Level?.
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