A plant produces aluminum, facing costs of C(A) = \frac{A^2}{10}, where A is the number of aluminum units produced, and selling them on the competitive market for a price \$ 30. A farmer grows beets next to the aluminum factory, facing costs of C(B) = 5B + \frac{B^2}{100} + \frac{A^2}{20}, where B is the number of beets produced, and selling them for \$ 15 on the competitive market. Because aluminum pollution is harmful to agricultural production, the state government imposes a tax on aluminum production. What is the socially optimal tax on aluminum?

Jose recently died with a probate estate of $900,000. he was predeceased by his wife, guadalupe, and his daughter, lucy. he has two surviving children, pete and fred. jose was also survived by eight grandchildren, pete’s three children, naomi, daniel, nick; fred’s three children, heather, chris and steve; and lucy’s two children, david and rachel. jose’s will states the following “i leave everything to my three children. if any of my children shall predecease me then i leave their share to their heirs, per stirpes.” which of the following statements is correct? (a) under jose’s will rachel will receive $150,000. (b) under jose’s will chris will receive $150,000. (c) under jose’s will nick will receive $100,000. (d) under jose’s will pete will receive $200,000.