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Q1 Answer All Questions [50%]

Consider two households: call them Household A and Household B. There are two periods in the world, t ∈ {0, 1}. Each household has preferences of the form

Ui(ci0,ci1(ω))=log(ci0)+βiEω log(ci1(ω))

for i ∈ {A, B} where ci0 denotes the household’s consumption in their first period of life and ci1(ω) is their consumption in the second period of life when state ω prevails. The parameter βi denotes the household’s discount factor, (notice that we allow this to potentially differ across the two households). We’ll consider an endowment economy where the households are each endowed with some amount of consumption goods in each period of life. Assume that there is no randomness regarding the world in period t = 0 but there are two states of the world at t = 1, denoted by ω ∈ {ω1,ω2}. Household i’s endowment of consumption goods in period t = 0 is denoted by ei0, while that of period t = 1 and state ω is denoted by ei1(ω) for i ∈ {A, B} and ω ∈ {ω1, ω2}. Assume that the endowments across the two households are asymmetric and negatively correlated across the two households, with their vectors of endowments given by

eA(eA0 , eA1 (ω1), eA1 (ω2)) = (1, 1, 0) eB(eB0 ,eB1 (ω1),eB1 (ω2)) = (1,0,2).

Assume that there are complete asset markets, where we denote household i’s holdings of state contingent claims for state ω as ai(ω). Also denote the prices for these state contingent claims as φ(ωi). State contingent claims are held in zero net supply. Assume that state ω eventuates at t = 1 with probability π(ω) where π(ω1) + π(ω2) = 1.

  1. Write-down and solve the optimisation problem faced by each household. Describe this in detail. How does this relate to real world investor decision problems? Give examples and details.
  2. Write-down the market clearing conditions for consumption goods and state contingent claims in periods t = 0 and t = 1. What do these represent? What are the implications if they don’t hold? How do they relate to real life financial transactions?
  3. Describe the competitive equilibrium price of each of the two state contingent claims. Give a thorough intuition for their solution and relate to the real world.
  4. Describe the concept of risk sharing. How would the situation differ in a scenario without complete asset markets? Map this to the real world with examples.
  5. Describe the nexus of corporate finance and asset pricing. Give examples from models and concepts from class and relate to the real world. 1

Q2 Answer All Questions [50%]

Give a detailed explanation of the difference between dividends and equity issuance (both initial public offerings and seasoned equity offerings). What are the financial frictions at play in driving firms’ decisions with regard to these two types of transactions?

Give responses in detail. Provide detailed answers, including equations, economic intuition, material from class and any other evidence to support your discussion. Answers will be assessed on the basis of insight, accuracy, creativity, attention to detail and relevance.

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