Consider a market with the following supply and demand functions:
QD = a0 – a1PD a0, a1 > 0
QS = b0 + b1PS b0, b1 > 0
(a) (8 marks) 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) (12 marks) 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 constrain 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.
Consider the following general form of a constant elasticity of substitution production function:
You may find this question easier to answer if you let α1 = δ1/ρ and α2 = (1−δ)1/ρ. By all means, leave your answer in terms of α1 and α2. Assume a firm is trying to minimize the cost of producing any given y. Costs are given by
C = wL + rK.
Find the firm’s cost minimizing demand function for L. The cost minimizing demand for K is determined simultaneously (so you need both FOCs) but since I am sure many of you left this until the last minute, you only have to come up with the expression for L. However, for your own practice, you may want to find the equivalent expression for K on your own. You may assume that nonnegativity constraints on L and K are not binding.
Any help with that? Thanks!