Two firms compete as a Stackelberg duopoly. The inverse market demand they face is P = 62 - 4.5Q. The cost function for each firm is C(Q) = 8Q. The outputs of the two firms are:
A. QL = 48; QF = 24.
B. QL = 35; QF = 6.
C. QL = 6; QF = 3.
D. None of the statements associated with this question are correct.
C. is the correct answer
To determine which option is correct, we need to calculate the total quantity demanded and the price in the market using the given inverse demand function. Then, we can compare the outputs of the two firms (QL and QF) from the options with our calculations.
The inverse demand function given is: P = 62 - 4.5Q.
To find the total quantity demanded in the market, we need to add the outputs of both firms: Q = QL + QF.
A. QL = 48; QF = 24.
QL + QF = 48 + 24 = 72.
B. QL = 35; QF = 6.
QL + QF = 35 + 6 = 41.
C. QL = 6; QF = 3.
QL + QF = 6 + 3 = 9.
Now we can substitute the total quantity Q into the inverse demand function to find the price:
P = 62 - 4.5Q.
A. P = 62 - 4.5(72) = 62 - 324 = -262 (not possible as price can't be negative).
B. P = 62 - 4.5(41) = 62 - 184.5 = -122.5 (not possible as price can't be negative).
C. P = 62 - 4.5(9) = 62 - 40.5 = 21.5 (possible).
Comparing the outputs of the firms and the calculated total quantity and price, we find that option C: QL = 6 and QF = 3, is the correct statement for this question.