Figure 14-10
In the figure below, panel (a) depicts the linear marginal cost of a firm in a competitive market, and panel (b) depicts the linear market supply curve for a market with a fixed number of identical firms.
-Refer to Figure 14-10. If there are 700 identical firms in this market, what is the value of Q1?
A)140,000
B)210,000
C)280,000
D)420,000

Question

Figure 14-10
In the figure below, panel (a) depicts the linear marginal cost of a firm in a competitive market, and panel (b) depicts the linear market supply curve for a market with a fixed number of identical firms.  
-Refer to Figure 14-10. If there are 700 identical firms in this market, what is the value of Q1?
A)140,000 
B)210,000 
C)280,000 
D)420,000

Quizplus · Accepted Answer

In a competitive market, the market supply curve is the horizontal sum of individual firm supply curves. Therefore, to find the market quantity supplied at a given price, we need to add up the quantities supplied by each firm at that price. 
In this figure, if there are 700 identical firms in the market, the market supply curve is the horizontal sum of 700 individual firm supply curves. From panel (a), we can see that each firm's supply curve intersects the price axis (i.e., marginal cost equals zero) at 50,000 units. Therefore, at a price of $4, the quantity supplied by one firm is 50,000 units. The quantity supplied by 700 firms would be 700 times 50,000, which equals 35,000,000 or 35 million units. 
From panel (b), at a price of $4, the market quantity supplied is 210,000 units. Therefore, to find the value of Q1, we need to solve for the value of Q such that the market quantity supplied equals 140,000. 
From panel (b), the equation for the market supply curve is Q = 234,000 + 90,000P. Setting Q equal to 140,000 and solving for P, we get P = $2. P = 2 is therefore the equilibrium price at which the market quantity supplied equals 140,000. 
To find the corresponding quantity supplied by each firm, we can plug P = $2 into the equation for individual firm supply curve in panel (a). The equation is Q = 50,000 + 20,000P. At P = $2, Q equals 90,000. Therefore, each firm supplies 90,000 units at a price of $2. 
Since there are 700 identical firms, the total quantity supplied at a price of $2 is 63 million units (700 times 90,000). To find the quantity supplied in the range between $2 and $4, we can subtract the quantity supplied at $2 from the quantity supplied at $4. We know that the quantity supplied at $4 (which we found earlier) is 35 million units. Therefore, the quantity supplied between $2 and $4 is 35 million minus 63 million, which equals -28 million units. This negative quantity implies that the firms would not supply anything in this range, since their marginal costs exceed the price. 
Therefore, the total quantity supplied in the market is 140,000 units.