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?

(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.