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Consider a monopoly host on Airbnb that sets both their nightly price (p) and their cleaning fee (f). However, Airbnb only reveals the nightly price to consumers so there is a chance that consumers do not account for the cleaning fee when making purchasing decisions. More specifically, suppose that demand is given by Q = 1-p-0.5-f; this demand system corresponds to a 50% chance that the consumer does not notice the additional cleaning fee when making purchasing decisions. Lastly, assume that host costs are zero so that the host has the following profit function: (p, f) = (p+f-0) Q = (p+f) (1-p-0.5-f). (Note there are no constraints in this problem).