Chris and Dana live in an exchange economy with two goods: good Q and good R. Chris startsoff with an endowment of 6 units of Q and 10 units of R. Dana starts off with an endowment of 8units of Q and 8 units of R.

1. Draw anEdgeworth box for this exchange economy, and label the initial endowmentwith a W. The box does not have to be exactly to scale, but it should be clear what the size of thebox is in terms of its width and height.

2. Suppose that Chris's utility function is given by U_C=Q_C^1/2R_C^1/2, whereQ_C andR_Care his consumption of Q and R, respectively. Dana's utility function is given byU_D=Q_D^1/3R_D^2/3, whereQ_D and R_Dare her consumption of Q and R, respectively.

What is the equation for themarginal rate of substitution (MRS) between Q and R for each of the two agents?

3. Suppose that the price of good R is p_R=1 and the price of good Q isp_Q=2.

How much is Chris's initial income, given his endowments and given these prices?

4. How much is Dana's initial income, given her endowments and given these prices?