Question

The group decides to raise money by selling t-shirts at a table on campus. It costs them $560 to stock 200 t-shirts and $420 to stock 100 t-shirts.  They decide to charge $5 for every t-shirt they sell.                                                                                                  

• What is the marginal cost for each t-shirt?
• The group also has set up costs that they need to pay like the renting of the table, printing posters and renting space from the university.  What are the fixed costs to set up the table?
• Write the cost function.
• Write the revenue function.
• How many t-shirts does the group have to sell in order to break even?
• Write the profit function.
• What is the profit if they sell 400 t-shirts?

Answer 1

(I) Marginal cost = Change in TC / Change in Q = $(560 - 420) / (200 - 100) = $140/100 = $1.4

(II) TC = F + v x Q where F: Fixed cost, v: AVC

420 = F + 100v........(1)

560 = F + 200v........(2)

(2) - (1) gives

100v = 140

v = 1.4 (= MC)

F = 420 - 100v = 420 - 140 = 390

(III) TC = 390 + 1.4Q

(IV) TR = P x Q = 5Q

(V) In break-even TR = TC

390 + 1.4Q = 5Q

3.6Q = 390

Q = 108.33

(VI) Profit = TR - TC = 5Q - 390 - 1.4Q = 3.6Q - 390

(VII) When Q = 400, Profit = (3.6 x 400) - 390 = 1440 - 390 = 1050