B, C, D
At present an individual is set to earn $20 today and $30 tomorrow and can borrow or lend at a rate of 20%. His intertemporal utility function is represented by u(x1,x2)=x121x221, where x1 is the amount an individual chooses to consume today and x2 is the amount an individual chooses to consume tomorrow. The individual also faces a human-capital production function 2x12+x22=1700. A. What consumption today and tomorrow will maximize the individual's lifetime income? B. In tomorrow's dollars, what is the individual's maximal lifetime income? C. What consumption today and tomorrow will maximize the individual's lifetime utility? D. Make a general graphical argument (i.e. relying on the graphical approach to optimization in this model and not necessarily specific to this exact utility function) as to whether an increase in the interest rate will increase or decrease an individual's final consumption today. If it is impossible to determine, show how an identical increase in the interest rate can lead to an increase or a decrease in today's consumption. At present an individual is set to earn $20 today and $30 tomorrow and can borrow or lend at a rate of 20%. His intertemporal utility function is represented by u(x1,x2)=x121x221, where x1 is the amount an individual chooses to consume today and x2 is the amount an individual chooses to consume tomorrow. The individual also faces a human-capital production function 2x12+x22=1700. A. What consumption today and tomorrow will maximize the individual's lifetime income? B. In tomorrow's dollars, what is the individual's maximal lifetime income? C. What consumption today and tomorrow will maximize the individual's lifetime utility? D. Make a general graphical argument (i.e. relying on the graphical approach to optimization in this model and not necessarily specific to this exact utility function) as to whether an increase in the interest rate will increase or decrease an individual's final consumption today. If it is impossible to determine, show how an identical increase in the interest rate can lead to an increase or a decrease in today's consumption
