Consider a situation where there are two goods: x and G. There are two individuals: 1 and 2. Each individual privately consumes x, and x2 of good x, respectively. In contrast, they both consume G amount of the second good. The price of good x is p, and each individual makes an income m, and m2 respectively. a. Suppose each individual contributes a different share to the aggregate good G. The share they contribute is t, of total G for individual 1, and tz of total G for individual 2. Write their budget constraints. [5 marks] b. Using the general utility functions u, (x1, G) and uz (x1, G), where the budget constraints are given above, write and describe the first order conditions for each individual. [10 marks] c. Suppose each individual could choose their own optimal level of G, so that individual 1 consumes an amount G, and individual 2 consumes an amount G2. Using the utility functions: uj (x1, G1) = a, In(G,) + In x] U2 (X2, G2) = a2 In(G2) + In x2 Solve for each consumer's optimal choice of G. [15 marks] d. Suppose we impose the constraint that G must be equal to the sum of the two individuals' contributions to G. Solve for the optimal level of G. [10 marks] e. Suppose in a society you had two individuals who wanted different quantities of a common good G so that G, > G2. How would you determine what value of G you would choose? Explain the logic behind your