A decision maker with an exponential u$-$function and a risk aversion coefficient,

$=0\mathrm{.}001,$ who is engaging in a sealed bid auction. The u$-$curve is$,$

$U(x)=1-$exp$(-x)$

The decision maker's PIBP for the bidding item is $$900,$ and believes that the maximum

competitive bid distribution is a scaled Beta $(10,10)$ distribution on a scale of $0$ to $1000,$

i$.$e$,(10,10,0,1000).$

Plot the Opposing forces of bidding $($i$.$e$.$ plot the cumulative distribution of the

maximum competitive bid vs$.$ bid, and the curve of $[$PIBP$-$bid$]$ vs$.$ bid$)$

Plot the certain equivalent of any bid vs$.$ the bid amount.

Determine the optimal bid for the decision$-$maker.

Determine the least amount of money that the decision maker needs to be paid in

order to not participate in this bidding situation.

Plot a sensitivity analysis for the optimal bid vs$.$ the risk aversion coefficient $($over

the range $0$ to $0\mathrm{.}1).$

From your plot, determine if the more risk averse people bid higher or lower than

the less risk averse people.

Plot a sensitivity analysis for value of bidding situation vs the risk aversion

coefficient $($over the range $0$ to $0\mathrm{.}1).$

Repeat parts $(3)$ and $(4)$ if the PIBP is $$400.$ Comment on the difference in the

results when the PIBP was $$900.$

Extra Credit: Plot a two$-$way sensitivity analysis for optimal bid vs both the risk

aversion coefficient and PIBP. Hint: This is a $3$D plot. If using Excel, you can use

a $2$Dimensional Data Table.