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Consider a firm operating in a competitive market in the short run. The table below shows the firm’s total cost of production at various output levels. Assume the firm cannot supply more than 7 units in the short run. At a market price of $9, how many units of output should the firm supply? Output (q) FC ($) VC ($)0 10 01 10 22 10 63 10 104 10 155 10 216 10 307 10 40

Question

Consider a firm operating in a competitive market in the short run. The table below shows the firm’s total cost of production at various output levels. Assume the firm cannot supply more than 7 units in the short run. At a market price of 9,howmanyunitsofoutputshouldthefirmsupply? Output(q)FC(9, how many units of output should the firm supply? Output (q) FC () VC ($)0 10 01 10 22 10 63 10 104 10 155 10 216 10 307 10 40

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Solution

To determine how many units of output the firm should supply, we need to compare the market price with the marginal cost (MC) of each additional unit of output. The marginal cost is the increase in total cost (TC) that results from producing one more unit of output. It can be calculated as the change in total cost divided by the change in quantity.

First, we need to calculate the total cost (TC) for each output level, which is the sum of fixed costs (FC) and variable costs (VC).

Output (q) FC ()VC() VC () TC ($) 0 10 0 10 1 10 2 12 2 10 6 16 3 10 10 20 4 10 15 25 5 10 21 31 6 10 30 40 7 10 40 50

Next, we calculate the marginal cost (MC) for each additional unit of output.

Output (q) TC ()MC() MC () 0 10 - 1 12 2 2 16 4 3 20 4 4 25 5 5 31 6 6 40 9 7 50 10

The firm should continue to produce as long as the market price is greater than or equal to the marginal cost. Given a market price of 9,thefirmshouldproduce6unitsofoutput.Atthisoutputlevel,themarginalcostofproducinganadditionalunitwouldbe9, the firm should produce 6 units of output. At this output level, the marginal cost of producing an additional unit would be 9, which is equal to the market price. Producing more than 6 units would result in a marginal cost greater than the market price, which would not be profitable for the firm.

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