Question

Assume a competitive firm faces a market price of ​$60​, a cost curve​ of: C​ = 0.003q cubed ​+ 25q ​+ 750​, and marginal cost curve​ of: MC​ = 0.009q2​ + 25. The​ firm's profit maximizing output level ​(to the nearest tenth​) is nothing ​units, and the profit ​(to the nearest penny​) at this output level is ​$ nothing. In this​ case, firms will enter exit . 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 ​$ nothing ​(round your answer to the nearest penny​). At this price level the profit will be the level of fixed cost the level of variable cost zero cannot be determined .

Answer 1

• In a competitive market firms individually face a perfectly elastic demand at the equilibrium price, which in this case is P=60. (Conceptually, this means that they cannot exert influence over prices, the price is fixed at equilibrium level).

• Then, the firm with the cost structure describe by C​ = 0.003q cubed ​+ 25q ​+ 750​ (total costs) and MC​ = 0.009q2​ + 25 (marginal cost), will produce the quantity for which price equals marginal cost (optimality condition).
• Then, according to optimality condition, firm should produce: 60= 0.009q2​ + 25 ⇒
  `q=\sqrt{ (60-35)/(0.009) }`, q≈62 units.
• In this case, firms will enter the market because average cost per unit produced (which can be calculated by dividing total cost by q), is AC≈49 for this specific firm (replace q=62 in the average cost function, that, as mentioned is just the total cost (C) divided by q (C/Q) and check it!), and average income per unit sold in the market is price, which is $60. It is profitable to sell in this market under this conditions!!
• This will cause market supply to shift to shift right (more firms entering the market imply an increase in market supply). This will continue until the price equals the minimum average cost of $47.5 (average cost is minimun when marginal cost equals marginal cost: this happends under the specified functions when q=50, and when q=50, average cost exhibits this value).
• At this price level the profit will be the level of fixed cost, and the level of variable cost (which can be defined as the part of the cost that depends only on the quantity produced, in this case VC=0.003q+25q) will be VC=0.003x50+25x50≈$1250.