2. Consider an economy consisting of two people, A and B who have utility functions and

endowments as follows: please see attached file!

a) Find the core of this economy and illustrate it in an Edgeworth Box diagram.

b) What is the Walrasian equilibrium of this economy?

c) Suppose we add two people to the above economy, C and D such that C and A have

identical preferences and endowments as do B and D. Can you find one allocation

in the core of the original economy of two individuals which is not in the core of

the economy consisting of all four of them?

3. Consider an economy of two people and two goods. Total initial resources are e1+e2 >>0.

Individuals have identical homothetic utility functions, ui(xi) = u(xi), where u is a

continuous, strongly increasing and strictly concave function.

a) Show that the Walrasian equilibrium price vector is independent of the initial

distribution of endowments.

b) Show that the set of Walrasian equilibrium allocations coincides with the diagonal

of the Edgeworth box.

Hint: recall that a homothetic utility function has the property that the MRS is constant

along rays through the origin. You might also find it easier to do part (b) before part (a).

4. Consider an economy of two people, A and B who have utility functions and

endowments as follows: see file

a) Illustrate the contract curve and the core in an Edgeworth box diagram.

b) Define the relative price: see file. Use the Kuhn-Tucker conditions to show that P=1 is a

general equilibrium price ratio.

c) Show that P =1.5 is also a GE price ratio.

d) What would you guess are all of the GE price ratios in this economy?

endowments as follows: please see attached file!

a) Find the core of this economy and illustrate it in an Edgeworth Box diagram.

b) What is the Walrasian equilibrium of this economy?

c) Suppose we add two people to the above economy, C and D such that C and A have

identical preferences and endowments as do B and D. Can you find one allocation

in the core of the original economy of two individuals which is not in the core of

the economy consisting of all four of them?

3. Consider an economy of two people and two goods. Total initial resources are e1+e2 >>0.

Individuals have identical homothetic utility functions, ui(xi) = u(xi), where u is a

continuous, strongly increasing and strictly concave function.

a) Show that the Walrasian equilibrium price vector is independent of the initial

distribution of endowments.

b) Show that the set of Walrasian equilibrium allocations coincides with the diagonal

of the Edgeworth box.

Hint: recall that a homothetic utility function has the property that the MRS is constant

along rays through the origin. You might also find it easier to do part (b) before part (a).

4. Consider an economy of two people, A and B who have utility functions and

endowments as follows: see file

a) Illustrate the contract curve and the core in an Edgeworth box diagram.

b) Define the relative price: see file. Use the Kuhn-Tucker conditions to show that P=1 is a

general equilibrium price ratio.

c) Show that P =1.5 is also a GE price ratio.

d) What would you guess are all of the GE price ratios in this economy?

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