For each of the following utility functions find the marginal utility and show that it is increasing at a decreasing rate. Mathematically, U'(W)>0 and U''(W)<0. Also graph each function to verify your results.
    Exponential    U(W)=e^(-AW)
    Logarithmic    U(W)=ln(W)
    Quadratic      U(W)=W-0.5AW^2
    Power          U(W)=(B/(B-1))*W^(1-1/B)
Describe a risk averse, a risk seeking and risk neutral investor.
what shape would the utility function of each be in risk-return space?
which best describes most people?
which is easiest to use?

Jake is degenerate gambler; he'll take abet on anything. Jake believes that if he spreads his bets around (diversifies) across many unrelated (ρ=0) games then he will make money. Show that Jake is incorrect when the bookie(TAB)has the edge.
Who is Jensen and why does he have an inequality?