Question

Assume a competitive firm faces a market price of $60, a cost curve of C = 0.004q^3 + 30q + 1000, and a marginal cost of curve of: MC = 0.009q^2 + 25.
a. The firm's profit maximizing output level (to the nearest tenth) is ___units, and the profit (to the nearest penny) at this output level is $____.
b. This will cause the market supply to (shift right/shift left). This will continue until the price is equal to the minimum average cost of $____.

Answer 1

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.