QUESTION TWO (11 pts). Now suppose a consumer derives their income from labor, l, priced at an (exoge- nous) wage rate of w. She uses this labor income to purchase a single consumption good, y, at price p, which she values alongside leisure, q, according to the utility function, u(c, q ) = yql-7. (i) (1 pts). Define the budget constraint of the agent. (ii) (3 pts). Suppose each unit of day can be split into labor I and leisure q. Defining leisure as q = 1 - l, set up the utility maximization problem of the consumer. (iii) (3 pts). Derive the utility-maximizing labor supply of the agent, I* (iv) (4 pts). Derive the utility-maximizing consumption demand of the agent, y*. How does it compare to the labor supply function