Math Solutions

[Step-by-Step] A firm has two factories, for which costs are given by: Factory 1:C_1(Q_1)=10Q_1^2 , Factory 2:C_2(Q_2)=20Q_2^2 , The firm faces the following

Question: A firm has two factories, for which costs are given by:

\[\begin{aligned} & \text{Factory 1}:{{\text{C}}_{\text{1}}}\left( {{\text{Q}}_{\text{1}}} \right)\text{=10Q}_{\text{1}}^{\text{2}} \\ & \text{Factory 2}:{{\text{C}}_{\text{2}}}\left( {{\text{Q}}_{\text{2}}} \right)\text{=20Q}_{\text{2}}^{\text{2}} \\ \end{aligned}\]

The firm faces the following demand curve:

\[P=700-5 Q\]

where \(Q\) is total output- i.e., \(Q=Q_{1}+Q_{2}\).

  1. On a diagram, draw the marginal cost curves for the two factories, the average and marginal revenue curves, and the total marginal cost curve (i.e., the marginal cost of producing \(\left.Q=Q_{1}+Q_{2}\right) .\) Indicate the profit-maximizing output for each factory, total output, and price.
  2. Calculate the values of \(Q_{1}, Q_{2}, Q\), and \(P\) that maximize profit.
  3. Suppose that labor costs increase in Factory 1 but not in Factory 2 . How should the firm adjust (i.e., raise, lower, or leave unchanged) the following: Output in Factory 1? Output in Factory 2? Total output? Price?

Price: $2.99
Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document


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