Under the Rug is a house-cleaning firm that uses only one input: labour. Under the Rug works with a large number of casual workers and can change the amount of labour em- ployed instantaneously. The market for house-cleaning services is perfectly competitive. Every day, Under the Rug incurs an administrative cost covering insurance, government registration costs, and membership fees for various professional associations. That cost is $60 and it is independent of the number of houses serviced. Under the Rug's daily wage bill as a function of the number of houses cleaned in a given day is summarised in the table below. Under the Rug has no other costs. Quantity Wages paid 1 $20 2 $50 3 $90 4 $140 5 $200 6 $270

(c) (4 marks) What is the minimum price in the market for cleaning services at which Under the Rug will clean at least one house daily? At what prices will Under the Rug shut down? Explain why. (d) (4 marks) Derive and draw the short-run supply curve of Under the Rug. Explain how you arrived at your answer

.(e) (3 marks) If the market price for house cleaning is $40, what is the profit-maximising number of houses cleaned by Under the Rug and what profits will it have?