Question 1 (Consumer Choice - Cobb-Douglas Utility with two goods) Alice has the utility function u(1,2)=2x112,...

  

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Question 1 (Consumer Choice - Cobb-Douglas Utility with two goods) Alice has the utility function u(1,2)=2x112, where 2₁ 20 and 22 20 are the amounts of the two goods that she consumes. 1/3 a) In a diagram with 22 on the vertical axis, sketch her indifference curve that corresponds to the consumption bundle A = (75,50) (i.e. the bundle with 75 units of good 1 and 50 units of good 2.) b) Find a consumption bundle B that contains more than 75 units of good 1 such that A is indifferent between the bundles A and B) B (i.e. Alice c) Find a consumption bundle C that contains more than 50 units of good 2 such that C B (ie. Alice is indifferent between the bundles C and B) d) Prove that A C for Alice. Sketch the bundles B and C in your diagram in part a. e) Use mathematical notation to write down the set S that contains all consumption bundles X= (1, ₂) for which XA. (i.e. the set that contains all consumption bundles which Alice strictly prefers over bundle A). Illustrate this set in your above graph. For the next parts adopt the assumption that both goods cost 2 dollars per unit. Moreover, suppose Alice spends exactly 100 dollars on these two goods every month. f) Write down the set B that contains all of the consumption bundles that Alice can afford, under the above assumptions. g) Find the consumption bundle O=(,) that Alice will choose, under the above assumptions to maximize her utility. h) Show that O is an element of B (i.e. show that O E B). Question 1 (Consumer Choice - Cobb-Douglas Utility with two goods) Alice has the utility function u(1,2)=2x112, where 2₁ 20 and 22 20 are the amounts of the two goods that she consumes. 1/3 a) In a diagram with 22 on the vertical axis, sketch her indifference curve that corresponds to the consumption bundle A = (75,50) (i.e. the bundle with 75 units of good 1 and 50 units of good 2.) b) Find a consumption bundle B that contains more than 75 units of good 1 such that A is indifferent between the bundles A and B) B (i.e. Alice c) Find a consumption bundle C that contains more than 50 units of good 2 such that C B (ie. Alice is indifferent between the bundles C and B) d) Prove that A C for Alice. Sketch the bundles B and C in your diagram in part a. e) Use mathematical notation to write down the set S that contains all consumption bundles X= (1, ₂) for which XA. (i.e. the set that contains all consumption bundles which Alice strictly prefers over bundle A). Illustrate this set in your above graph. For the next parts adopt the assumption that both goods cost 2 dollars per unit. Moreover, suppose Alice spends exactly 100 dollars on these two goods every month. f) Write down the set B that contains all of the consumption bundles that Alice can afford, under the above assumptions. g) Find the consumption bundle O=(,) that Alice will choose, under the above assumptions to maximize her utility. h) Show that O is an element of B (i.e. show that O E B).

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