Question

In perfectly competitive market, we sum horizontally individual firms’ marginal cost curves and use it as an approximation of the market supply curve. Give justifications for this method.

Answer 1

In order to maximize profit a perfect competitive firm produces that quantity at which P = MC where P = Price and MC = Marginal Cost which is a function of Quantity(Q) or we can say that MC(Q) meaning Marginal cost of producing Q_th unit of output

Thus we have P = MC(Q) --------------------------------------------(1)

So, above relationship tells us the amount of quantity producer is willing to supply at different Price level.

Suppose There are n firms.

At P = P₁. Firm 1 is producing Q₁₁ , Firm 2 is producing Q₂₁ , Firm 3 is producing Q₃₁ , ------------ Firm n is producing Q_n1

So For Firm i we have ;

P₁ = MC_i(Q_i1) where MC_i represents Marginal cost function of i_th firm , quantity supplied by i_th firm is Q_i1 and horizontal value of MC_i(Q_i1) = Q_i1(Quantity supplied by firm i at P = P₁)

Thus using (1) we have

Market supply at (P = P₁ ) = Q₁₁ + Q₂₁ -----------------------------+ Q_n1

Similarly, Market supply at P = P₂ = Q₁₂ + Q₂₂ -----------------------------+ Q_n2

Similarly Market supply at P = P_k = Q_1k + Q_2k -----------------------------+ Q_nk

Thus At any price P total quantity supplied will be horizontal summation of the individual firm's Marginal cost curves.