Suppose that there are only 10 individuals in the economy each with the following utility function over present and future consumption:

Suppose that there are only 10 individuals in the economy each with the following utility function over present and future consumption: , where  is consumption today, and  is consumption tomorrow. Consumption tomorrow is less valued because people are impatient and prefer consuming now rather than later. Buying 1 unit of consumption today costs $1 today and buying 1 unit of consumption tomorrow costs $1 tomorrow. All individuals have income of $10 dollars today and no income tomorrow (because they will be retired) but they can save at the market interest rate 

.

What is the price today of one unit of consumption tomorrow?

Calculate the price today of one unit of consumption tomorrow if .

Calculate the maximum you can consume today if you consume  tomorrow and the interest rate is 

How much of his or her income will an individual consume today given that the interest rate is 0.3?

How much of his or her income will an individual consume today given that the interest rate is 0.5?

How much of his or her income will an individual consume today given that the interest rate is 0.7?

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