For this question, you will need to comment on (and perform calculations with) the following possible utility functions. U(W)=WU(W)=W2U(W)=a+bWcW2,(c>0)U(W)=1W11,(>1) Part A (4 marks): Check if each utility function satisfies monotonicity. Part B (3 marks): Briefly explain why a utility function of wealth (i.e., whose argument is wealth) should satisfy monotonicity. Hint: one way to think about this would be to assume the contrary and argue why this would be unreasonable. Part C ( 6 marks): For utility functions that satisfy monotonicity, determine whether the function describes risk-averse, risk-neutral, or risk-loving preferences. Hint: approach this question in two steps, i) mathematically define risk-averse, risk-neutral, and risk-loving preferences, and ii) use these definitions to determine which type of preferences each function represents