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Nazarene
Nazarene
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Hi, everyone! I'd appreciate some help with this problem, please.

Suppose that a seller puts a one-unit good on the market, and a buyer comes around with an unknown valuation $θ$. This buyer has a quasi-linear utility function $θq-p,$ and costs are quadratic with $c(q) = \dfrac{1}{2}q^2.$

Now suppose that $θ$ is uniformly distributed on $[0,1].$

Find the optimal direct mechanism $(p(·),q(·)).$

At the moment, I understand that we would need to maximize the seller's expected revenue, though I am not sure to navigate this problem. All help is appreciated.

everyone! I'd appreciate some help with this problem, please.

Suppose that a seller puts a one-unit good on the market, and a buyer comes around with an unknown valuation $θ$. This buyer has a quasi-linear utility function $θq-p,$ and costs are quadratic with $c(q) = \dfrac{1}{2}q^2.$

Now suppose that $θ$ is uniformly distributed on $[0,1].$

Find the optimal direct mechanism $(p(·),q(·)).$

At the moment, I understand that we would need to maximize the seller's expected revenue, though I am not sure to navigate this problem. All help is appreciated.

 

Hi, everyone! I'd appreciate some help with this problem, please.

Suppose that a seller puts a one-unit good on the market, and a buyer comes around with an unknown valuation $θ$. This buyer has a quasi-linear utility function $θq-p,$ and costs are quadratic with $c(q) = \dfrac{1}{2}q^2.$

Now suppose that $θ$ is uniformly distributed on $[0,1].$

Find the optimal direct mechanism $(p(·),q(·)).$

At the moment, I understand that we would need to maximize the seller's expected revenue, though I am not sure to navigate this problem. All help is appreciated.

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Nazarene
Nazarene
  • 23
  • 4

(Mechanism Design | Mailath Exercise 10.5.3) A Question

everyone! I'd appreciate some help with this problem, please.

Suppose that a seller puts a one-unit good on the market, and a buyer comes around with an unknown valuation $θ$. This buyer has a quasi-linear utility function $θq-p,$ and costs are quadratic with $c(q) = \dfrac{1}{2}q^2.$

Now suppose that $θ$ is uniformly distributed on $[0,1].$

Find the optimal direct mechanism $(p(·),q(·)).$

At the moment, I understand that we would need to maximize the seller's expected revenue, though I am not sure to navigate this problem. All help is appreciated.