This question will help us understand the difference between market supply (QS)

Question

This question will help us understand the difference between market supply (QS) and an individual firm’s supply (qS). Suppose that there are three firms with different cost functions and associated marginal costs given below:

C1(q) = 20 + q + 3q2

C2(q) = 30 + 2q + q2

MC1(q) = 1 + 6q MC2(q) = 2 + 2q

C3(q) = 10 + 1q2 42

MC3(q) = 1q

a) (2 Points) What do we mean by an individual firm’s supply function qS(P)?

b) (2 Points) In terms of the market price p, solve for each firm’s individual supply function.

c)(2 Points) Note that the market supply function is just the sum of all individual firm’s supply functions. Determine the market supply function.

Explanation / Answer

(a) Individual firm's supply curve describes the quantity supplied by an individal firm at each price level. It is upward rising and is that portion of Marginal cost (MC) curve that is higher than the minimum Average variable cost (AVC) curve, because if Price falls below the AVC, the firm will shut down.

(b)

For firm 1, Supply function: P = MC1, or P = 1 + 6q1 [Or, q1 = (P - 1) / 6]

For firm 2, Supply function: P = MC2, or P = 2 + 2q2 [Or, q2 = (P - 2) / 2]

For firm 3, Supply function: P = MC3, or P = q3 [Or, q3 = P]

(c)

Market supply function is horizontal summation of individual supply functions.

Market supply, Q = q1 + q2 + q3

Q = [(P - 1) / 6] + [(P - 2) / 2] + P

Q = [(P - 1) + (3P - 6) + 6P] / 2

Q = (10P - 7) / 2

[Equivalently,

2Q = 10P - 7

10P = 2Q + 7

P = (2Q + 7) / 10 = 0.2Q + 0.7]

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