Answer all parts (a)-(g) of this question.Mette has started Mersea Oysters. She aims to export oysters to Germany where she acts as aprice taker. After a couple of nights of calculations she believes that her cost function is givenby C(q) = 100 + 6q + 2q2, where q denotes kilos of oysters harvested. The market price shewill face in Germany is 50 per kilo.(a) [4 marks] Derive Mette’s marginal cost function.(b) [7 marks] Use your result from (a) to determine the profit-maximizing output level.(c) [7 marks] Explain in words why the supply function for a price taker is the same as themarginal cost function.(d) [8 marks] Calculate Mette’s profit. Illustrate marginal cost and profit in a diagram.(e) [8 marks] Now instead assume that the price is 22. Should Mette produce at this price?(f) [8 marks] Assume again that the price is 22 but that the fixed cost of producing (100) issunk and was taken in the previous period. Should Mette produce at this price in this case?(g) [8 marks] Assume again that the price is 50 but a tax of 28 per kilo oysters sol d is introducedon imported oysters in Germany. Should Mette sell oysters in Germany?
Answer all parts (a)-(g) of this question.
Mette has started Mersea Oysters. She aims to export oysters to Germany where she acts as a
price taker. After a couple of nights of calculations she believes that her cost function is given
by C(q) = 100 + 6q + 2q2, where q denotes kilos of oysters harvested. The market price she
will face in Germany is 50 per kilo.
(a) [4 marks] Derive Mette’s marginal cost function.
(b) [7 marks] Use your result from (a) to determine the profit-maximizing output level.
(c) [7 marks] Explain in words why the supply function for a price taker is the same as the
marginal cost function.
(d) [8 marks] Calculate Mette’s profit. Illustrate marginal cost and profit in a diagram.
(e) [8 marks] Now instead assume that the price is 22. Should Mette produce at this price?
(f) [8 marks] Assume again that the price is 22 but that the fixed cost of producing (100) is
sunk and was taken in the previous period. Should Mette produce at this price in this case?
(g) [8 marks] Assume again that the price is 50 but a tax of 28 per kilo oysters sol d is introduced
on imported oysters in Germany. Should Mette sell oysters in Germany?
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