1. Lauren has an estate of $12 million. She is deciding how much to donate to a non-profit organization (n) and to her children (c). Her utility function is u(c, n) = Vcn сп. Estates are taxed at a...

please answer all three i, ii, and iii with explanations.

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Extracted text: 1. Lauren has an estate of $12 million. She is deciding how much to donate to a non-profit organization (n) and to her children (c). Her utility function is u(c, n) = Vcn сп. Estates are taxed at a rate of 50%, but $E of an estate is exempt from the tax. Donations to the non-profit are also exempt from the tax. So, the estate pays tax at a rate of 50% on the value of the estate after the donation has been made to the non-profit organization, and $E of the estate is exempt from the tax. Assume that E is less than 12 million. (i) Find the kink point in the budget set. For which values of E will Lauren's estate pay some tax? (ii) Find the optimal bundle. (iii) Suppose that the estate tax is repealed. Find the optimal bundle now. Does the donation to the non-profit organization rise or fall when the estate tax is repealed?