This question examines a perfectly competitive firm in the market for soap. You will use the market equilibrium price and rm-specic cost functions to identify the protmaximizing output ofa perfectly competitive rm and examine whether market entry or exit is likely. Sam's Soap is one of many producers in the perfectly competitive soap market Sam's Soap is a pricetaking firm. and the equilibrium market price for a bar of soap is $3. Suppose that the marginal cost of producing soap at Sam's Soap is ME = Q! 10, where Q is the numb er of bars of soap that the rm produces. Task 1: Identify the protmaximising number of soap bars that Sam's Soap should produce. Task 2: When Sam's Soap produces the protmaximizing number of soap bars, how much total revenue does it earn? Task 3: Suppose the total cost Sam's Soaps incurs can be expressed as TC = 2GB + 013'20, where Q is the number of bars of soap that the rm produces. When Sam's Soap produces the prot-maximizing number of soap bars, how much to tal cost does it incur? Task 4: Suppose the total cost Sam's Soaps incurs can be expressed as TC = EDS + QEIEO, where Q is the number of bars of soap that the rm produces. When Sam's Soap pmduees the protmaximising number of soap bars, how much prot does it earn? Task 5: Based on your answers above. would you expect new firms to enter the perfectly competitive market, or would you expect some existing rms to exit? Explain your answer carefully