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Supply and Demand Functions in Equilibrium

Consider a market with the following supply and demand functions:

QD = a0 - a1PD a0, a1 > 0

QS = b0 + b1PS b0, b1 > 0

(a) Find the equilibrium quantity and price as a function of the parameters (use any method you like). Are there any additional restrictions that you must impose on the parameters for this model to make sense?

(b) Now assume the government imposes a per unit tax t on the market. One economic view of government (made famous by noble prize winner James Buchanan) is the Leviathan view of government. This approach assumes government wants to become as large as possible, subject to a utility constraint (if the utility of citizens falls too low, people will rise up and constrain the Leviathan). Thus, government will try to maximize tax revenues subject to the utility constraint. Here we will consider a simple case were the utility constraint is not binding and can be ignored. Suppose the Leviathan government is trying to maximize its revenues from a specific tax t in a market with the demand and supply functions given above. Find an expression for the tax revenue (e.g. tQ) maximizing t in terms of the parameters of the model

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The following posting discusses questions regarding supply and demand functions.

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