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This is a question comes from Field Exam in Advanced Economics Theory (Jan 2016) from UCB Econ Dept. In the first problem (Q1), it asks:

b) How does welfare relative to the full information welfare depend on $\alpha$ and $\delta$?

I have never seen such expression before. What does the phrase "welfare relative to the full information welfare" mean?

My wild guess is to set up the total welfare as a function of $\alpha$ and $\delta$? Thanks in advance.

Edit 1.

I am asked to "type the question out so that we don't have to follow a link to see it." So here it goes:

Consider a two period bargaining model in which an uninformed buyer makes offers. If there is trade in period 1 the payoffs are ${\alpha}q-p$ for the buyer and $p-q$ for the seller where $p$ is the price and $q$ is the quality and ${\alpha}.0$. We assume the realization of q is only known to the seller and drawn from a Uniform $(0,1)$. If instead they trade in the second period their payoffs from a time zero perspective are ${\delta}({\alpha}q-p)$ and ${\delta}(p-q)$ for ${\delta}\in [0,1]$ and if they don't trade they get 0.

a) Show that the equilibrium will be characterized by two cutoff types $q_1({\alpha};{\delta}) \in [0,1]$ and $q_2({\alpha};{\delta})\in [q_1,1]$ such that types $q < q_1$ trade in the first period and that types $q$ such that $q_1\leq q \leq q_2$ trade in second period and finally types above $q_2$ do not trade.

b) How does welfare relative to the full information welfare depend on $\alpha$ and $\delta$?(If you find this hard to do analytically, at least work out a few examples with low and high values and explain)

c) Assume ${\alpha} = 1.7$ and ${\delta} = 0.8$ and suppose that with probability ${\gamma}$ in the second period another buyer arrives in the market in which case, they both simultaneously submit offers to the seller. How does welfare relative to the full information welfare depend on ${\gamma}$? (Do only the ${\gamma} = 1$ case if you are short on time.)

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  • $\begingroup$ Hi. Welcome to Economics.SE. Please type out the question so that we don't have to follow a link to see it. Economics.SE has mathjax support, so you should be able to type out all of the latex. $\endgroup$ – cc7768 May 10 '16 at 1:20
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What it means is the following:

Consider the same bargaining game played by two players that are fully informed (i.e. the buyer is also informed about the value of $q$). Then find the equilibrium of this game and calculate welfare. This is the ``full information welfare'' that the question refers to.

Then solve the model where only the seller is informed about the value of $q$ i.e. find the equilibrium of this game. Now calculate equilibrium welfare. How does it compare to the one you calculated for the full-information case? I would probably do this by calculating the fraction $$\frac{\text{Asymmetric info welfare}}{\text{Full info welfare}}.$$

Lastly, you need to see how this fraction changes as the values of $\alpha$ and $\delta$ change.

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