Question

Suppose Dan's cost of making pizzas is

C(Q)=8Q+(Q2/160),C(Q)=8Q+(Q2/160),

and his marginal cost is

MC=8+(Q/80).MC=8+(Q/80).

Dan is a price taker.

a. What is Dan's supply function?

Q = 160P + 640 if P ≥ 8. | |

Q = 80P - 640 if P ≥ 8. | |

Q = 80P - 160 if P ≥ 10.5. | |

Q = 80P + 640 if P ≥ 8. | |

Q = 80P - 80 if P ≥ 10.5. |

b. What if Dan has an avoidable fixed cost of $250? What is Dan's
supply function?

Q = 80P + 640 if P ≥ 10.5. | |

Q = 160P + 80 if P ≥ 8. | |

Q = 160P - 640 if P ≥ 10.5. | |

Q = 80P - 640 if P ≥ 10.5. | |

Q = 80P - 160 if P ≥ 8. |

Answer #1

With no avoidable fixed cost, total cost is C = 8Q + Q^2/160 and MC = 8 + Q/80

Supply function is P = MC

8 + Q/80 = P

Minimum price is minimum AVC which is 8

P – 8 = Q/80

Q = 80P – 640

Hence the correct supply function is Q = 80 – 640 if P > 8

Now avoidable fixed cost is 250 so cost function is C = 8Q + Q^2/160 + 250

AC = 8 + Q/160 + 250/Q

Minimum price is minimum AC

1/160 = -250/Q^2

Q = 200 units

AC(Q = 200) = 10.5

Hence now supply function is Q = 80 – 640 if P > 10.5

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