Two local ready-mix cement manufacturers,Here and There,have combined demand given by Q = 105 - P.Their total costs are given by TC_Here = 5Q_Here + 0.5Q²_Here and TC_There = 5Q_There + 0.5Q²_There.If they cannot successfully collude and instead produce where the market price equals marginal cost,their total output will be: A) 50. B) 60. C) 66.67. D) 75. E) 85.

Question

Quizplus · Accepted Answer

The first step is to find the individual marginal cost (MC) for each manufacturer. 
MCHere = 5 + 0.5QThere 
MCThere = 5 + 0.5QHere

To find the total output, we need to solve for the equilibrium price and quantity: 
Q = 105 - P

Setting MCHere = P and solving for QHere: 
5 + 0.5QThere = 105 - QHere 
1.5QHere + 0.5 QThere = 100 
QHere = (100 - 0.5QThere)/1.5

Setting MCThere = P and solving for QThere: 
5 + 0.5QHere = 105 - QThere 
1.5QThere + 0.5 QHere = 100 
QThere = (100 - 0.5QHere)/1.5

To find the total output, we add QHere and QThere: 
QTotal = QHere + QThere 
QTotal = (100 - 0.5QThere)/1.5 + (100 - 0.5QHere)/1.5 
QTotal = (200 - 0.5(QHere + QThere))/1.5 
QTotal = (200 - 0.5QTotal)/1.5 
QTotal = 66.67

Therefore, the total output when they produce where the market price equals marginal cost is 66.67, which is choice C.

Two Local Ready-Mix Cement Manufacturers,Here and There,have Combined Demand Given