a) You know that a household's utility function is given by either u1(x1, x2) = ln x1 + In X2, U2 (21,x2) = x1 + 2x2 or uz (21,x2) = x1 + VC2 . Based on the household's choices, you are able to infer the following about the household's preferences: (3,3) > (1,2) ~(2,1) > (1,1). Which utility function is the correct one? Explain. b) Draw the indifference curves that includes the bundle (4,4) for the following utility functions: U4 (21,22) = 2x1 + x2, U5 (21,22) = 12122, U6 (x1, x2) = min{x1,222} c) Calculate the MRS at the bundle (4,1) for the following utility functions: U4 (x1, x2) = 2x1 + x2 and u6 (21 , x2) = min{x1,2x2}. How does the MRS change with x as you move along the indifference curve? d) Do the following following utility functions describe preferences that are monotonic and convex? Explain! U7 (21,22) -(x1 + x2 20)2 + 400 U8 (21,x2) V x+ x = = a) You know that a household's utility function is given by either u1(x1, x2) = ln x1 + In X2, U2 (21,x2) = x1 + 2x2 or uz (21,x2) = x1 + VC2 . Based on the household's choices, you are able to infer the following about the household's preferences: (3,3) > (1,2) ~(2,1) > (1,1). Which utility function is the correct one? Explain. b) Draw the indifference curves that includes the bundle (4,4) for the following utility functions: U4 (21,22) = 2x1 + x2, U5 (21,22) = 12122, U6 (x1, x2) = min{x1,222} c) Calculate the MRS at the bundle (4,1) for the following utility functions: U4 (x1, x2) = 2x1 + x2 and u6 (21 , x2) = min{x1,2x2}. How does the MRS change with x as you move along the indifference curve? d) Do the following following utility functions describe preferences that are monotonic and convex? Explain! U7 (21,22) -(x1 + x2 20)2 + 400 U8 (21,x2) V x+ x = =