Question

Petra run her own business producing jewelry. She works out of her dorm room and paid $200 for a soldering gun. In addition, she buys raw materials for each unit of jewelry produced and uses her own time to both develop designs and produce jewelry. The total cost of raw materials and the time spent by Petra to produce q units of jewelry  . Marginal cost is given by MC(q)=5+2q.

a. Find expressions for Petra’s fixed cost, average fixed cost, total cost, average total cost and average variable cost as a function of output. In addition, find the level of output at which average total cost is minimized.

b. Provide at least one example of each of the following: an additional fixed/variable/sunk cost that might be associated with a jewelry-making business.

Answer 1

a) Fixed cost = $ 200 for soldering gun

Average fixed cost = Fixed cost / quantity = 200/q

Total cost = Total fixed cost + Total variable cost = 200 + (5q + q2) = 200 + 5q + q2

Average total cost = Total cost / Quantity = (200 + 5q + q2) / q

Average variable cost = Total variable cost / quantity = (5q + q2)/q = 5 + q

ATC = (200 + 5q + q2) / q

ATC = 200/q + 5 + q

dATC/dq = -200/q2 + 0 + 1 = 0

- 200/q2 = - 1

-q2 = - 200

q = $10\sqrt{2}$

d2ATC/dq2 = 400/q3 is positive which means ATC is minimized at q = $10\sqrt{2}$ units.

b) Fixed cost is the rent paid for the space.

Variable cost includes Sales commission, advertising expenses.

Expenditure on buying soldering gun is sunk ost of firm.