Answer:
a) q = $62.36
b) As the profit level is NEGATIVE ( π = - 99.21 ), this will cause the market supply to shift left. This will continue until the price is equal to the minimum average cost of $60.
Explanation:
Given that; the market price P = $60
The cost curve is C = 0.004q³ + 30q + 1000
The marginal cost of curve of MC = 0.009q² + 25
We know that the condition for the profit maximizing level of output is MC=P
∴ 0.009q² + 25 = 60
0.009q² = 35
q² = 35 / 0.009
q² = 3888.88888
q = √3888.88888
q = $62.36
Now we calculate profit at the equilibrium output
π = TR -TC
π = ( P × Q ) - TC
we know TC = 0.004q³ + 30q + 1000
now we substitute
so π = ( 60 × 62.36 ) - { 0.004(62.36)³ + 30(62.36) + 1000
= 3741.6 - ( 970.01 + 1870.8 + 1000
= 3741.6 - 3840.81
π = - 99.21
As the profit level is NEGATIVE, the supply curve shifts left
Average cost is the cost per unit of output.
Average Cost = TC / q
Average Cost = (0.004q³ + 30q + 1000) / q
Average Cost = 0.004q² + 30 + 1000/q
Now equate the derivative of AC with zero
i.e ΔAC/Δq = 0
Δ/Δd{ 0.004q² + 30 + 1000/q } = 0
0.008q - 1000/q² = 0
0.008q = 1000/q²
0.008q³ = 1000
q³ = 125000
q = ∛125000
q = 50
Average cost at this point will be
AC = 0.004q² + 30 + 1000/q
= 0.004 (50)² + 30 + 1000/50
= 10 + 30 + 20
= $60
As the profit level is NEGATIVE ( π = - 99.21 ), this will cause the market supply to shift left. This will continue until the price is equal to the minimum average cost of $60.
