Question

In: Economics

(2) Jurian has preferences u J (x J 1 ; x J 2 ) = (x...

(2) Jurian has preferences u J (x J 1 ; x J 2 ) = (x J 1 ) 4 (x J 2 ) 2 . (a) Find his uncompensated demand for the two goods as a function of prices and her wealth w. (b) Find his compensated demand as a function of prices and her utility u. (c) Now suppose that Jurian interacts with Katinka in an exchange economy, where Katinka’s preferences are u K(x K 1 ; x K 2 ) = min[2x K 1 ; 2x K 2 ]. Both have endowment (1, 1). Draw the Edgeworth box for this economy, including both people’s endowments and indifference curves. (d) What is the competitive equilibrium of this economy? Is it Pareto efficient? You can take as given that Katinka’s uncompensated demand function is x K(p1, p2; e K 1 , eK 2 ) = ( e K 1 p1 + e K 2 p2 p1 + p2 , e K 1 p1 + e K 2 p2 p1 + p2 )

Expert Solution

Individual 1's preferences can be represented by the following utility function:

a. Uncompensated Demand:

The individual's problem is:

At equilibrium, marginal rate of technical substitution is equal to the ratio of the prices of the two goods:

Substituting this value in the consumer's budget constraint:

b. Compensated Demand:

Tangency condition will be satisfied:

Substituting this into the utility function:

c.

d. Taking the price of good 2 as numeraire. Total demand for good 1 is equal to total endowment:

At this price, demands for both goods by individuals one and two are:

This allocation is Pareto Efficient.

Rahul Sunny answered 1 year ago

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