Please explain how Jack and Cody  can maxmise utility through living in the same household with a unitary and non-unitary models. Unitary models - Mutual altruism (or any unitary model) Non-unitary models - Copertive models - Collective + Bargaining model.(or any Non-unitary models)

Ma1. Please give only typed answer.

5.18 In a two-good, two-consumer economy, utility functions are u¹ (x₁, x₂) = x₁(x₂)², u² (x₁, x₂) = (x₁)²x₂. Total endowments are (10, 20). (a) A social planner wants to allocate goods to maximise consumer 1's utility while holding con- sumer 2's utility at u² = 8000/27. Find the assignment of goods to consumers that solves the planner's problem and show that the solution is Pareto efficient. (b) Suppose, instead, that the planner just divides the endowments so that e¹ = (10, 0) and e² = (0, 20) and then lets the consumers transact through perfectly competitive markets. Find the Walrasian equilibrium and show that the WEAs are the same as the solution in part (a).

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In a standard economic model, we generally assume the individual only cares about their own payoff. So, for example, utility of individual i is given by u = pi, where pi is the individual’s payoff. Suppose the individual is playing a dictator game with another partner j. How would you modify the utility function to explain the non-zero allocations to the partner that are typically observed?

Economics Explain in detail how you would extend the Cox- Ross{Rubinstein binomial tree model for pricing options if instead of considering two states of nature in each period you consider three states of nature (e.g. a good state, a middle state and a bad state). Focus on a tree with two periods (periods 0, 1 and 2) and draw the corresponging trinomial tree.