Econ 450 HW 1 - Econ 450 Autumn 2016 HW 1 1 Consider the following market for a private good where Anne and Beverlys demand curves are given by PA = 25

# Econ 450 HW 1 - Econ 450 Autumn 2016 HW 1 1 Consider the...

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Econ 450 Autumn 2016 HW 1 1. Consider the following market for a private good, where Anne andBeverly’s demand curves are given by PA= 25-QPB= 25-5QThe marginal cost of this good isMC= 2Q(a) Calculate the market demand curve 2 points.(b) Depict this market graphically. 3 points.(c) Calculate the market price and quantity that will be produced,assuming this market is perfectly competitive. 3 points.(d) Argue that this outcome is efficient, both in productive efficiencyand exchange efficiency.. 2 points. 2. Define and explain what aPareto improvementis, using anEdgeworthBox. 5 points. 3. Consider a consumer with the following preferences: U(x, y) = 20 logx+ywho face pricespx= 10,py= 10, and has wealthw= 100.(a) Write the consumer maximization problem, with all constraints.5 points.(b) Construct the Lagrangian, and solve for the optimal choices ofxandy. Verify that you have included the appropriate constraints.15 points.

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