4. Worth 25 points total. Consider an economic agent who has instantaneous utility function where: C, and G, are consumption goods (variables). Let the price of these goods be given respectively by pc, and pot, and assume that the agent's income is It. This agent treats the prices of goods as well as income as given (i.e., they are exogenous variables from the agent's perspective). The agent's utility maximization problem can be stated formally as max 0.569.5 Ct. Gt such that Pct . C + PG. . G. SI, (a) Set up the Lagrangian associated with this problem. (Hint: because instantaneous utility is increasing and concave in each of its arguments, then the constraint will bind-that is, it will hold with equality.) (b) Use the Lagrangian to derive mathematically the agent's optimal consumption of each good. (c) Use your answer to (b) to derive mathematically the agent's optimal level of instantaneous utility