Cost Curves: You own a small accounting firm that prepares tax forms for medium
ID: 1208573 • Letter: C
Question
Cost Curves:
You own a small accounting firm that prepares tax forms for medium sized businesses.
Your accounting firm uses accountants (input L) and computer systems (input K), with production
function y=20*K^0.25L^0.25, where y is clients served. You can change the number of accountants and
computer systems whenever you want. You also rent an office for $900,000; in order to help any
clients you must have an office but the required size of your office does not vary with the number of
clients. The yearly wage of an accountant is wL=$400,000, the cost of a computer system (including
software, furniture, and hardware) for one year is wK=$100,000. Assume that your accounting firm
is a pricetaker.
a. What is the cost function for your business for one year?
b. Assume you have already paid the office rent for one year (you were required to pay in
advance). What is the equation of your shortrun supply curve and at what minimum price
will you operate (do business)?
c. Graph your average cost curve, average variable cost curve, and your longrun supply curve.
At what minimum price will you operate in the longrun?
d. If the market price for serving a client is p=¥100,000, what is your longrun producer
surplus? Hint: use your longrun supply curve to calculate producer surplus. ALSO, what is
your profit?
Explanation / Answer
a) Cost of fim = fixed cost + variable cost = rent office + wage * no. of accountants + price of computer*no. of computers
= 90,000 + 400,000L + 100,000K.
b) Short run supply curve is the MC curve above AVC curve
At minimum price wage/price of computer = MP of accountant/MP of computer
400,000/10,000 = K0.25K0.75 / L0.25L0.75
K/L = 4/1
K = 4L
thus employing 4 accoutans at each coumputer will be optimal.