Question 3
Mr. Richie was a wealthy business man. He had two children, Janet
and Jackson. Richie has \(\theta\) gold necklaces and \(\theta\) diamond rings. In this economy, Mr. Richie was the
only consumer who had gold necklaces and diamond rings. Mr. Richie did not write any will. When
he died, half of his gold necklaces were inherited by Janet, and the other half by Jackson. Similarly,
half of his diamond rings were inherited by Janet and the other half by Jackson. Janet and Jackson
did not have any other assets and did not receive anything else from Mr. Richie.
(a)
Draw an Edgeworth Box with two consumers, Janet (lower left) and Jackson
(upper right), and two goods, gold necklaces (horizontal axis) and diamond rings (vertical
axis). Locate the endowment bundles in the Edgeworth Box, after Janet and Jackson receive
their father's assets.
(b)
Suppose a gold necklace is more expensive than a diamond ring. Draw a new
Edgeworth Box showing Janet's and Jackson's budget sets.
(c) Suppose that Janet only cares about diamond rings, Jackson only cares about gold necklaces
and Janet and Jackson can trade among themselves.
(d)
(i)
(ii)
(iii)
Draw a new Edgeworth Box showing: (I) two of Janet's indifference curves
including an arrow pointing towards the direction of higher utility, and (II) two of
Jackson's indifference curves including an arrow pointing towards the direction of higher
utility (use a different colour).
Is there any competitive equilibrium in which gold necklaces and diamond
rings have the same price? Explain and illustrate your answer. If your answer is yes,
identify Janet's and Jackson's competitive allocations.
Is there any competitive equilibrium in which gold necklaces are more expensive
than diamond rings? Explain and illustrate your answer. If your answer is yes, identify
Janet's and Jackson's competitive allocations.
Draw a new Edgeworth Box showing the set of Pareto Optimal allocation(s).
