Candice and Dominica are engaged in exchange over two goods: boxes of pens (x) and boxes of paper (y). They both have inequality averse preferences as defined by the following equation. di[u¡(xi, yi), uj(xj, yj)]= u¡ — 8¡max[u¡ — u¡, 0]—a¡max[u¡ — uj, 0] We assume that a; and 8; are identical for Candice and Dominica. In this interaction, the two players each treats themselves as player i and their co-participant as player j. The two players have the following initial endowments. Candice has 16 boxes of pens and 4 of paper. Dominica has 4 of boxes pens and 46 of paper. a. Graph the Edgeworth box for the exchange between Candice and Dominica when they each have utilities that are Cobb-Douglas and take the following form: U₁ = x₁² Y₁

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Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.13P
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Question 4 (Please note that part a, b, and c are independent questions.
Answer all parts)
Part A [Word limit 500]
Candice and Dominica are engaged in exchange over two goods: boxes of pens (x)
and boxes of paper (y). They both have inequality averse preferences as defined by
the following equation.
d¡ [u¡(Xi, Yi), Uj(xj, y¡)]= u¡ — 8¡max[u¡ — u¡, 0]—α¡max [u¡ — Uj,
-
-
o]
We assume that a; and 8; are identical for Candice and Dominica. In this interaction,
the two players each treats themselves as player i and their co-participant as player
j.
The two players have the following initial endowments. Candice has 16 boxes of
pens and 4 of paper. Dominica has 4 of boxes pens and 46 of paper.
a. Graph the Edgeworth box for the exchange between Candice and Dominica
when they each have utilities that are Cobb-Douglas and take the following
form:
1
U₁ = x² y}
y²
Candice knows Dominica's utility takes this form, and vice versa. They use
this information when constructing their ; functions. Derive the equation of
the contract curve. In your Edgeworth box, show their initial allocations, their
initial indifference curves, and the contract.
b. Referring to your Edgeworth box, explain the shape of the indifference curves
and how we determine a Pareto efficient allocation in the Edgeworth box.
c. What would happen if a; increased? Explain by referring to your Edgeworth
box. It is useful to think about what happens to marginal utility with changes in
the consumption of pens and paper when a; changes.
Part B [Word limit: 500]
d. Leaving for holidays, Emma's luggage may be lost with probability p = 0. 1.
The luggage and its content are estimated to be worth £316.05. Emma's utility
function over monetary payoffs is given by u(x)=√x. Suppose Emma can
insure against the loss of the luggage, what is the maximum insurance
premium / that Emma would be willing to pay?
e. Using a diagram show and explain that a risk loving individual would decline
the offer of full insurance coverage on actuarially fair terms.
Transcribed Image Text:Question 4 (Please note that part a, b, and c are independent questions. Answer all parts) Part A [Word limit 500] Candice and Dominica are engaged in exchange over two goods: boxes of pens (x) and boxes of paper (y). They both have inequality averse preferences as defined by the following equation. d¡ [u¡(Xi, Yi), Uj(xj, y¡)]= u¡ — 8¡max[u¡ — u¡, 0]—α¡max [u¡ — Uj, - - o] We assume that a; and 8; are identical for Candice and Dominica. In this interaction, the two players each treats themselves as player i and their co-participant as player j. The two players have the following initial endowments. Candice has 16 boxes of pens and 4 of paper. Dominica has 4 of boxes pens and 46 of paper. a. Graph the Edgeworth box for the exchange between Candice and Dominica when they each have utilities that are Cobb-Douglas and take the following form: 1 U₁ = x² y} y² Candice knows Dominica's utility takes this form, and vice versa. They use this information when constructing their ; functions. Derive the equation of the contract curve. In your Edgeworth box, show their initial allocations, their initial indifference curves, and the contract. b. Referring to your Edgeworth box, explain the shape of the indifference curves and how we determine a Pareto efficient allocation in the Edgeworth box. c. What would happen if a; increased? Explain by referring to your Edgeworth box. It is useful to think about what happens to marginal utility with changes in the consumption of pens and paper when a; changes. Part B [Word limit: 500] d. Leaving for holidays, Emma's luggage may be lost with probability p = 0. 1. The luggage and its content are estimated to be worth £316.05. Emma's utility function over monetary payoffs is given by u(x)=√x. Suppose Emma can insure against the loss of the luggage, what is the maximum insurance premium / that Emma would be willing to pay? e. Using a diagram show and explain that a risk loving individual would decline the offer of full insurance coverage on actuarially fair terms.
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