What would be the annual cost saved by shifting from the -bag lot size to the EOQ? The annual holding cost with the EOQ is $
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Answer:
q1 = 910
q2 = 910
Explanation:
Given:
Q = 2800 - 1000p
Marginal cost = $0.07 per unit
Q = 2800 - 1000p
Let's calculate profit of firm 1:
TR = p1 q1
MR = MC = 0.07
Cross multiplying:
2800 - 2q₁ - q₂ = 70
2800 - 2q₁ = 70 + q₂
2800 - 70 - 2q₁ = q₂
2730 - 2q₁ = q₂...............(1)
Let's calculate profit of firm 2:
TR = p₁ q₂
MR = MC = 0.07
Cross multiplying:
2800 - q₁ - 2q₂ = 70
2800 - 2q₂ = 70 + q₁
2800 - 70 - 2q₂ = q₁
2730 - 2q₂ = q₁................... (2)
Substitute 2730 - 2q₂ for q₁ in (1)...
Thus:
2730 - 2q₁ = q₂
2730 - 2(2730 - 2q₂) = q₂
2730 - 5460 + 4q₂ = q₂
-2730 + 4q₂ = q₂
-2730 = q₂ - 4q₂
-2730 = - 3q₂
q₂ = -2730/-3
q₂ = 910
Substituting 910 for q₂ in (2):
2730 - 2q₂ = q₁
2730 - 2(910)= q₁
2730 - 1820 = q₁
910 = q₁
q₁ = 910
The Cournot equilibrium quantities are: q₁= 910; and q₂ = 910