2. Jeremy has preferences over electricity (E) and solar power (S) that can be represented by U(S, E) = (81 + F1). His income is $120, the price of a unit of electricity is $2, and the price of a unit of solar power is $4. (a) Suppose the government offers a per unit subsidy for solar power. Specifically, for every unit of solar power Jeremy buys, he receives $2 from the government. (This effectively lowers the price Jeremy pays for solar power to $2.) Use the Lagrangian method to derive Jeremy's optimal bundle given this subsidy. (b) Now suppose instead that the government simply gives Jeremy a lump sume of $60 to be spent as he sees fit. (This effectively raises his income to $180.) What bundle will be now choose? You are not required to use the Lagrangian method to answer this part of the question. (c) On one graph, depict Jeremy's utility maximizing bundles from parts (a) and (b), using budget lines and indifference curves. Clearly illus- trate which bundle he prefers