1. Carmen and Dobbin consume cheese (c) and wine (w). Carmen's utility function is UC (c, w) = Inc+w. Dobbin's utility function is UP (c, w) = c²w. Carmen has 38 pounds of cheese and 3 litres of wine while Dobbin has no cheese and 27 litres of wine. • Draw the Edgeworth box for Carmen and Dobbin and shade all the allocations that Pareto dominate the initial endowment. • Draw the contract curve. • Find the competitive equilibrium price ratio and allocation. 2. Consider an exchange economy with two agents, Dan and Eve, and two goods, meat (m) and cabbage (c). Initially, Dan has 60 pounds of meat and 90 pounds of cabbage while Eve has 90 pounds of meat and 60 pounds of cabbage. Dan's utility function is UD (mp, cp) = (mp)²cp where mp and cp are the quantities of meat and cabbage (in pounds) he consumes and Eve's utility function is UE (mE, CE) = min{2mE, CE}, where me and CE are the quantities of meat and cabbage (in pounds) she consumes. (1) Draw the Edgeworth box of the exchange economy and shade all the allocations that Pareto dominate the initial endowment. (2) Derive the set of Pareto optimal allocations and draw the contract curve. (3) Find the competitive equilibrium price ratio and allocation.
1. Carmen and Dobbin consume cheese (c) and wine (w). Carmen's utility function is UC (c, w) = Inc+w. Dobbin's utility function is UP (c, w) = c²w. Carmen has 38 pounds of cheese and 3 litres of wine while Dobbin has no cheese and 27 litres of wine. • Draw the Edgeworth box for Carmen and Dobbin and shade all the allocations that Pareto dominate the initial endowment. • Draw the contract curve. • Find the competitive equilibrium price ratio and allocation. 2. Consider an exchange economy with two agents, Dan and Eve, and two goods, meat (m) and cabbage (c). Initially, Dan has 60 pounds of meat and 90 pounds of cabbage while Eve has 90 pounds of meat and 60 pounds of cabbage. Dan's utility function is UD (mp, cp) = (mp)²cp where mp and cp are the quantities of meat and cabbage (in pounds) he consumes and Eve's utility function is UE (mE, CE) = min{2mE, CE}, where me and CE are the quantities of meat and cabbage (in pounds) she consumes. (1) Draw the Edgeworth box of the exchange economy and shade all the allocations that Pareto dominate the initial endowment. (2) Derive the set of Pareto optimal allocations and draw the contract curve. (3) Find the competitive equilibrium price ratio and allocation.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:1. Carmen and Dobbin consume cheese (c) and wine (w). Carmen's utility function is
UC (c, w) = ln c+w. Dobbin's utility function is UD (c, w) = c²w. Carmen has 38 pounds of
cheese and 3 litres of wine while Dobbin has no cheese and 27 litres of wine.
• Draw the Edgeworth box for Carmen and Dobbin and shade all the allocations that
Pareto dominate the initial endowment.
. Draw the contract curve.
• Find the competitive equilibrium price ratio and allocation.
2. Consider an exchange economy with two agents, Dan and Eve, and two goods, meat
(m) and cabbage (c). Initially, Dan has 60 pounds of meat and 90 pounds of cabbage
while Eve has 90 pounds of meat and 60 pounds of cabbage. Dan's utility function is
UD (mD, CD) = (mp)²cp where mp and cp are the quantities of meat and cabbage (in
pounds) he consumes and Eve's utility function is UE (mê, cê) = min{2mã, câ}, where må
and CE are the quantities of meat and cabbage (in pounds) she consumes.
(1) Draw the Edgeworth box of the exchange economy and shade all the allocations that
Pareto dominate the initial endowment.
(2) Derive the set of Pareto optimal allocations and draw the contract curve.
(3) Find the competitive equilibrium price ratio and allocation.
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