Cardboard boxes are produced in a perfectly competitive market. Each identical firm has a short-run total...

Cardboard boxes are produced in a perfectly competitive market. Each identical firm has a short-run total cost curve of TC = 2Q^3 - 12Q^2 + 10Q + 20 where quantity is measured in thousands of boxes per week. The marginal cost of production is given by MC = 6Q^2 -24Q + 10. Calculate the price below which a firm in the market will not produce
any output (the shut-down price).

Solutions

Expert Solution

In short run, firm can bear the loss of fixed cost but it will not bear the loss of variable cost. Firm will continue to produce as long as it is able recover the variable cost.

Total Variable cost =2Q^3 - 12Q^2 + 10Q

Average Variable cost (AVC) = TVC/Q

= (2Q^3 - 12Q^2 + 10Q ) / Q

= 2Q^2 - 12Q + 10

On differentiating AVC, we get minimum point

dC/dq = 4Q - 12

P = 4Q -12

Price should not fall below the minimum point of AVC.

Rahul Sunny answered 1 year ago

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