Question 1.
EverClean Services provides daily cleaning maintenance of toilets in food courts in Singapore. Dozens of firms provide similar service. The service is standardised; each company cleans the toilets and maintains the proper levels of cleanliness. The service is typically sold as a one-month contract. The market price for the one-month service contract is $120 per toilet.
EverClean Services has fixed costs of $30,000. The manager of EverClean has estimated the following average variable cost (AVC) function for the firm, using data for the last two years:
AVC = 130 - 0.2Q +0.0005Q2
where AVC is measured in dollars and Q is the number of toilets serviced each month. Each of the estimated coefficients is statistically significant at the 5% level.
1. (a) Given the estimated AVC, define the marginal cost function for EverClean?
2. (b) By applying a suitable optimization procedure, derive the output level at which the AVC reaches its minimum value. What is the value of AVC at its minimum point?
3. (c) Should the manager of EverClean continue to operate, or should the firm shut down? Explain.
4. (d) The manager of EverClean finds two output levels that appear to be optimal. Show what these levels of output are, and explain which one is actually optimal.
5. (e) Calculate the profit (or loss) that the manager of EverClean Services can expect.