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political economy, Microeconomics

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Consider the model of corruption explored by Shleifer and Vishni’s where there is one government-produced good X. There is a demand for that good described by the inverse demand equation Qd = 10 – P. The official government price for the good is Pg=3. The government pays the cost of producing the good. A bureaucrat can restrict the supply of X. The fact that there are no risks of detection gives this public official incentives to ask for a bribe to supply the good. Consider the model of “no theft” where the consumer pays the official government price plus a bribe in order to obtain X. Assume that the official marginal revenue for selling the good in this context is given by Qc=(7/2) – (1/2)P.
In the model of “no theft” what is the amount of the bribe that the corrupt official will charge??

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