Question

Explain the relationship between the marginal cost curve of an individual firm and the short run market supply curve in a perfect competition industry.

Answer 1

Answer

In perfect competition, all firms produce identical goods whose market price is settled by total supply and demand in the market, and all firms are price taker.At that market price, each firm can supply whatever it wants.But the profit maximizing quantity is that amount of quantity where marginal cost(MC) is equal to marginal revenue(MR) of the firm, which is equal to the market price(P).

Total revenue(TR)= P*Q

MR is change in TR due to one additional unit change in quantity(Q)

MR= TR/Q , stands for 'change'

or, MR = (P*Q) / Q = P*Q/Q = P , as P is given

Average revenue (AR) = TR divided by total quantity

AR = P*Q/Q= P

in perfect competition, MR=AR=P

Now Total Cost(TC) = Total Fixed Cost(TFC) + Total Variable Cost (VC) ,or, simply Fixed cost(FC)+ Variable Cost(VC)

Now, Average total Cost(ATC) or Average Cost(AC) = TC/Q

Or, AC = (FC+VC)/Q = FC/Q+ VC/Q

Or, AC = AFC+AVC , AFC= Average Fixed Cost, and AVC= Average Variable Cost

MC is the change in total cost due to one additional unit change in quantity.

MC=TC/Q.

Now fixed cost is fixed for all units of output in short-run, so MC changes because of the change in variable cost of production.

So, MC=(FC+VC)/Q

or, MC=FC/Q+ VC/Q

or, MC= 0+ VC/Q, as FC is fixed ,FC =0

MC= VC/Q

The MC first declines with each additional unit of output. This happens because of the rising marginal productivity of the factors of production.But in the short run, at least one of the factors remain fixed and so the marginal productivity of the variable factors first increases, then reaches maximum, and then declines. Similarly, the MC first decreases, reaches minimum, and then rises for each additional unit of output.AVC and ATC orTC decline first, reaches their minimum and then increases.But MC reaches minimum before the AVC and ATC.. ATC or TC reaches its minimum after MC and AVC because of the gradual decline of AFC (ATC is the sum of AFC and AVC). MC reaches minimum first because of the diminishing marginal returns to scale or the decline in the variable factors' productivity.

Let labor (L) is the variable factor of production, and MP_L is the marginal productivity of labor.

MP_L (Q/L) decreases, as Q decreases , and MC( TC/Q) rises.

Now all these things give us the following cost curves under perfectly competitive market in figure-1

Figure-1

Points, a,b, and e are the minimum points of MC,AVC, and ATC/AC respectively.The MC curve cuts the AVC and ATC at their minimum points. Price is given in the market , and the firm is price taker. The profit maximizing quantity with respect to the given price is the minimum point of AVC where the MC cuts it. The horizontal line from P₁ is also the MR line (MR=P₁) which is also the demand curve of the firm under perfect competition.At this price, the demand curve is perfectly elastic.Now the firm can supply at any point on the upward sloping portion of the MC curve above 'b'. Above point 'b', it shows that Price(P)>AVC.

The firm will start to supply from point 'b'. Any point above that MR(=price)>MC. Point below the 'b' or , say at P₀ price, AVC>MR. It indicates firm's loss. So only that upward portion of the MC curve, that cuts the minimum point of AVC, is the supply curve of firm under perfect competition.

Market supply curve.

Figure-2

Figure-2 shows the market supply curve. The firms have identical cost function. If there are N number of firms, the market supply, i.e the total supply of the quantity would be the sum of the individual firm's supply.

So market supply Q_N= Q₁ + Q₂ +...............+Q_N

In figure-2 , we see that the market supply starts at price P₁. SS is the market supply curve. So the upward portion of the MC curve that starts from the minimum point of AVC curve is the firm's supply curve. If there are N number of firms in the market, then, SS is the market supply curve.

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