Consider an exchange economy with two consumers: Charlotte and Dylan, and two goods: quinoa (Q) and raspberries (R). Charlotte has an initial endowment of 99.6 units of quinoa and 76 raspberries. Dylan has 124.4 units of quinoa and 78.1 raspberries.
Charlotte’s utility function is given by UC=QC1/2 RC1/2 , where QC and RC are her consumption of Q and R, respectively. Dylan’s utility function is given by UD=QD1/3 RD2/3, where QD and RD are his consumption of Q and R, respectively.
Suppose that the market price of quinoa is pQ=2 and the market price of raspberries is pR=1.
- What is the value of Charlotte’s endowment, in dollar terms, given these market prices? [Use up to two decimal points in all of your answers below.]
- What is the value of Dylan’s endowment, in dollar terms, given these market prices?
- At these prices, how many units of Q would Charlotte want to consume? [Hint: Use the utility maximizing condition for Charlotte, along with her budget constraint.]
- At these prices, how many units of R would Charlotte want to consume?
- At these prices, how many units of Q would Dylan want to consume?
- At these prices, how many units of R would Dylan want to consume?
- At these prices, does the market clear? Explain how you reach your conclusion.
