DriveEasy Chauffeur Services (DCS) Pte Ltd is a company offering high-end limousine chauffeuring services in Singapore catering to busy executives who need to attend multiple business engagements during business hours. Dozens of firms compete in the same sector, and the services overlap with those provided by some taxi companies as well. For busy executives moving to meetings, the attractiveness is in not having to worry about parking. In addition, by not having to negotiate peak-hour congestion, they can even have discussions while being chauffeured to venues. The service is standardized; with DCS providing a vehicle and trained chauffeur for each 8-hour contract. The service is typically sold as a one-month contract. The market price for the one-day 8-hour service contract is $125 per client.
DCS has fixed costs of $4,500. The management has estimated the following average variable cost (AVC) function for the firm, using data for the last two years:
AVC = 133 – 0.15Q +0.00045Q2
where AVC is measured in dollars and Q is the number of clients serviced each business day. Each of the estimated coefficients is statistically significant at the 5% level.
(a) Given the estimated AVC, define the marginal cost function for DCS.
(b) By applying a suitable optimization procedure, calculate the output level at which the AVC reaches its minimum value. What is the value of AVC at its minimum point?
(c) The manager of DCS finds two output levels that appear to be optimal. Define these two levels?
(d) Compute the average variable costs corresponding to each of these two levels of output, and explain which level of output the firm will choose.
DCS has fixed costs of $4,500. The management has estimated the following average variable cost (AVC) function for the firm, using data for the last two years:
AVC = 133 – 0.15Q +0.00045Q2
where AVC is measured in dollars and Q is the number of clients serviced each business day. Each of the estimated coefficients is statistically significant at the 5% level.
(a) Given the estimated AVC, define the marginal cost function for DCS.
(b) By applying a suitable optimization procedure, calculate the output level at which the AVC reaches its minimum value. What is the value of AVC at its minimum point?
(c) The manager of DCS finds two output levels that appear to be optimal. Define these two levels?
(d) Compute the average variable costs corresponding to each of these two levels of output, and explain which level of output the firm will choose.
Asked Feb 24, 2013
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