Question

1. Inverse demand is P = 245 – 2Q and inverse supply is P = 20 + Q. a. What is the equilibrium price and quantity in this market? b. Graph the supply and demand curves, correctly identifying the intercepts and equilibrium. c. Is the equilibrium quantity in the elastic, unit elastic, or inelastic portion of the demand curve? Explain. d. Suppose inverse supply changes to P = 10 + 0.5Q. Is this an increase or decrease in supply? Graph the new supply curve, correctly identify the equilibrium price and quantity. e. Is the total revenue greater at this new equilibrium relative to the total revenue at the equilibrium in part a? Explain.

Answer #1

a)

P ($) | Qd | Qs |

20 | 112.5 | 0 |

50 | 97.5 | 30 |

95 | 75 | 75 |

140 | 52.5 | 120 |

185 | 30 | 165 |

245 | 0 | 225 |

Equilibrium price = 95 and equilibrium quantity = 75 (At equilibrium: Demand = Supply)

Total revenue = 95 x 75 = $7125

b)

c) Price elasticity = dQ/dP x Pe/Qe = -0.5 x 95/75 = -0.63

Therefore, the equilibrium quantity lies in the inelastic portion of the demand curve. (abs(PE) < 1)

d)

This is an increase in supply as supply curve shifts to the right (more is supplied at every price level)

Equilibrium quantity = 94, equilibrium price = 57

e)

Total revenue (new equilibrium) = 94 x 57 = $ 5358

This is less than the total revenue calculated in part a)

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