Here is the model as described in the photo of the attached document.

I would like help with these questions.

1. Give a rigorous definition of the market equilibrium of this economy.

2. Formulate the problem of the social planner of this economy

3. Define the first-order conditions associated with an interior solution. Give an economic interpretation of each of these conditions.

4. Are these conditions sufficient to characterize the resource allocation of the decentralized equilibrium of the economy Why?