A student has preferences over attending lectures on economics, x, and other occupations, y, represented by utility function : u(x, y) = y (1/2)x 2 . a) [5 marks] Accurately sketch indifference curves for utility levels u = 1 and u = 2 in the xy-space. What can you conclude about the students preferences for attending lectures on economics ? b) [5 marks] Find an equation for this individuals MRS, and provide an intuitive explanation for it in the context of your sketch in a). c) [5 marks] Suppose now further that the other occupations, y, consist of cycling, c, and dancing, d, where y c 1/3d 2/3 . The student has a daily endowment of 16 hours to be divided between cycling, dancing, and attending lectures on economics. Going for a bicycle ride takes 1.5 hours, dancing takes 1 hour, and lectures on economics last 3 hours. Write this students time constraint. d) [10 marks] The student must now optimize her choices of cycling, dancing, and lectures given her time constraint. Using the optimization technique of your choice, find this optimum : that is, find values (x , c , d ) that maximize her utility subject to the time constaint found in c).

Question 2 [25 marks] A student has preferences over attending lectures on economics, x, and other occupations, y, represented by utility function : u(x,y)=y(1/2)x2. a) [5 marks] Accurately sketch indifference curves for utility levels u=1 and u=2 in the xy-space. What can you conclude about the student's preferences for attending lectures on economics? b) [5 marks] Find an equation for this individual's MRS, and provide an intuitive explanation for it in the context of your sketch in a). c) [5 marks] Suppose now further that the other occupations, y, consist of cycling, c, and dancing, d, where yc1/3d2/3. The student has a daily endowment of 16 hours to be divided between cycling, dancing, and attending lectures on economics. Going for a bicycle ride takes 1.5 hours, dancing takes 1 hour, and lectures on economics last 3 hours. Write this student's time constraint. d) [10 marks] The student must now optimize her choices of cycling, dancing, and lectures given her time constraint. Using the optimization technique of your choice, find this optimum : that is, find values (x,c,d) that maximize her utility subject to the time constaint found in c ). Question 2 [25 marks] A student has preferences over attending lectures on economics, x, and other occupations, y, represented by utility function : u(x,y)=y(1/2)x2. a) [5 marks] Accurately sketch indifference curves for utility levels u=1 and u=2 in the xy-space. What can you conclude about the student's preferences for attending lectures on economics? b) [5 marks] Find an equation for this individual's MRS, and provide an intuitive explanation for it in the context of your sketch in a). c) [5 marks] Suppose now further that the other occupations, y, consist of cycling, c, and dancing, d, where yc1/3d2/3. The student has a daily endowment of 16 hours to be divided between cycling, dancing, and attending lectures on economics. Going for a bicycle ride takes 1.5 hours, dancing takes 1 hour, and lectures on economics last 3 hours. Write this student's time constraint. d) [10 marks] The student must now optimize her choices of cycling, dancing, and lectures given her time constraint. Using the optimization technique of your choice, find this optimum : that is, find values (x,c,d) that maximize her utility subject to the time constaint found in c )