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2 April, 13:51

Assume a European company that manufactures decorative fountain pens. The firm is trying to decide whether or not to expand its facilities. Currently, its fixed costs are $750,000 per month, and its average variable costs are $1.25 per pen. If the firm expands, its fixed costs will increase by $350,000 per month but its average variable costs will fall to $0.75 per pen.

a. Write out the formula for the firm's current (short run) total cost TC (q), and its (short run) total cost TC (q) if it expands, with q measures the number of pens per month.

b. Suppose the firm has a monthly volume of 600,000 pens. Should it expand? What about if the firm expects its volume to increase to 800,000 pens a month?

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  1. 2 April, 13:53
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    (a)

    TC (q) [before expansion] = Fixed Cost + Variable Cost

    = 750,000 + 1.25q

    TC (q) [after expansion] = (750,000 + 350,000) + 0.75q

    = 1,100,000 + 0.75q

    (b) (i) q = 600,000

    TC (q) [before expansion] = 750,000 + (1.25 * 600,000)

    = 750,000 + 750,000

    = 1,500,000

    TC (q) [after expansion] = 1,100,000 + (0.75 * 600,000)

    = 1,100,000 + 450,000

    = 1,550,000

    Since expansion will increase total cost, profit will fall ceteris paribus. So firm should not expand.

    (ii) q = 800,000

    TC (q) [before expansion] = 750,000 + 1.25 * 800,000

    = 750,000 + 1,000,000

    = 1,750,000

    TC (q) [after expansion] = 1,100,000 + (0.75 * 800,000)

    = 1,100,000 + 600,000

    = 1,700,000

    Since expansion will decrease total cost, profit will rise ceteris paribus. So firm should expand.
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