The firm Ragnar has announced an initial public offering of shares $($IPO$).$ Theshares are being offered in the IPO at a price of $$6$ each. All potential investorsknow that at this price the share is either undervalued by $$0\mathrm{.}50($probability $60\%)$or overvalued by $$0\mathrm{.}30($probability $40\%).$Informed investors such as banks are able to distinguish whether the share isovervalued or undervalued. Uninformed investors are not able to do this. Demand from uninformed investors is sufficient to take up all the shares offered in the IPO. If the demand for the shares is greater than the number offered, the shares will be rationed.You are an uninformed investor with $$12,000$ to invest. If rationing occurs you willonly be able to buy $800$ of Ragnar's IPO shares.$($a$)$ By what percentage is the IPO underpriced$/$overpriced$?(3$ marks$)($b$)$ What would be your expected profit if you were able to buy $2,000$ of the IPOshares? Do you expect to be able to do this? Why$/$why not?$(5$ marks$)($c$)$ As an uninformed investor, what is your expected profit from participating inthe IPO?$(5$ marks$)($d$)$ What would your expected profit be if the undervaluation is only $$0\mathrm{.}20$ pershare instead of $$0\mathrm{.}50,$ and everything else unchanged? What is theunderpricing percentage now? $(5$ marks$)($e$)$ Explain what is meant by the winner's curse in the context of IPOs, withreference to your answers for the previous parts of the question. Briefly discuss one other possible reason for the empirically observed underpricing of IPOs.