Chris and Dana live in an exchange economy with two goods: good????

Q

and good????

R

. Chris starts off with an endowment of 6 units of????

Q

and 10 units of????

R

. Dana starts off with an endowment of 8 units of????

Q

and 8 units of????

R

.

(a) [2 points] Draw an Edgeworth box for this exchange economy, and label the initial endowment with a W. The box does not have to be exactly to scale, but it should be clear what the size of the box is in terms of its width and height.

(b) [5 points] In equilibrium, what relationship must hold between Chris and Dana's Marginal Rates of Substitution? Explain intuitively why this is the case, and why the equilibrium is Pareto efficient.

(c) [2 points] Draw another Edgeworth Box and, using indifference curves for the two agents, illustrate one point that satisfies the equilibrium condition above, and label it with an E.

(d) [6 points] Suppose that Chris's utility function is given by????

????

=????

1/2

????

????

1/2

????

U

C

=

Q

C

1

/

2

R

C

1

/

2

, where????

????

Q

C

and????

????

R

C

are his consumption of????

Q

and????

R

, respectively. Dana's utility function is given by????

????

=????

1/3

????

????

1/3

????

U

D

=

Q

D

1

/

3

R

D

1

/

3

, where????

????

Q

D

and????

????

R

D

are her consumption of????

Q

and????

R

, respectively. What is the marginal rate of substitution (MRS) between????

Q

and????

R

for each of the two agents?

(e) [2 points] Suppose that the price of good????

R

is????

????

=1

p

R

=

1

and the price of good????

Q

is????

????

=2

p

Q

=

2

. Compute Chris and Dana's initial income, given their endowments and given these prices.

(f) [6 points] At these prices, how many units of????

Q

and????

R

would Chris want to consume? How many would Dana want to consume?