If a representative firm with total cost given by TC = 20 + 20q + 5q² operates in a competitive industry where the short-run market demand and supply curves are given by Q_D = 1,400 - 40P and Q_S = -400 + 20P,the number of firms operating in the short run will be:

Question

Quizplus · Accepted Answer

To determine the number of firms operating in the short run, we need to find the equilibrium price where the market demand and supply curves intersect. 
1,400 - 40P = -400 + 20P 
1,800 = 60P 
P = 30

Substituting P into the market demand curve gives us the equilibrium quantity: 
QS1U1B1DS1U1B0 = 1,400 - 40(30) = 1,200

To find the number of firms, we divide the equilibrium quantity by the output of one firm: 
Q/S1 = 1,200 / (S1S1P0) 
TC = 20 + 20q + 5qS1U1P12S1S1P0 
MC = 20 + 10q + 5qS1U1P12S1S1P0

Setting MC equal to the market price ($30), we solve for q: 
20 + 10q + 5qS1U1P12S1S1P0 = 30 
15q + 100S1U1P12S1S1P0 = 300 
q = (300 - 100S1U1P12S1S1P0) / 15

Substituting q into the expression for the number of firms: 
Q/S1 = 1,200 / [(300 - 100S1U1P12S1S1P0) / 15] 
Q/S1 = 48 - 16S1U1P12S1S1P0

Thus, the number of firms operating in the short run is Q/S1 = 48 - 16S1U1P12S1S1P0. 
If we set S1U1P12S1S1P0 = 0 (i.e. no fixed costs), we get: 
Q/S1 = 48

Therefore, the number of firms operating in the short run is 48, which is closest to choice C (200).

If a Representative Firm with Total Cost Given by TC