The market inverse demand curve is P = 90 – Q, where Q is the total market output consisting of Firm 1's output, q1, and Firm 2's output, q2. Both firms have a constant marginal cost of $10. If Firm 1 selects its output level first, how much output does each firm produce?

Firm 1 produces 40 and Firm 2 produce 20

Explanation:

Given that:

The market inverse demand curve is P = 90 – Q

Total TC = 10q + 10

and θ = q₁ + q₂

Both firms have a constant marginal cost

Then :

TC₁ = 10q₁ + 10

TC₂ = 10q₂ + 10

If Firm 1 selects its output level first, then it acts as a leader and firm 2 acts as a follower.

So, let have :

Ф₂  = pq₂  - TC₂

Ф₂  =  (90 - θ)q₂ - 10q₂ - 10

Ф₂  = 90q₂ - (q₁ + q₂)q₂  - 10q₂ - 10

Ф₂  =  80q₂  - q₁q₂ - q₂² - 10

80 - q₁ - 2q₂ = 0

80 - q₁ = 2q₂

2q₂= 80 - q₁

Ф₁ = pq₁- TC₁

Ф₁ = ( 90 - θ )q₁ - 10q₁ - 10

Ф₁  = 90q₁ - (q₁ + q₂)q₁  - 10q₁ - 10

Ф₁  = 80q₁ - q₁² - q₁q₂ - 10

Replace the value of q₂ in the above equation ,

40 - q₁= 0

q₁ = 40

Recall that

q₂ = 20

Firm 1 produces 40 and Firm 2 produce 20

the investment was $14,174.196

explanation:

a lump sum means that the father of the example made one deposit and leave it be.

we need to know the value of a capital that generated at 4.05% per year during 28 years the sum of $48,613.24

now clearing the formula to solve for capital we got:

and we reach the answer investment = $14,174.20

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