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Unformatted text preview: 's utility to be a fixed level). The optimal solution to this formulation cannot be improved upon (i.e. Pareto optimal allocation). [d] The production side of the economy can be succinctly described by a PPF. We write the equation of the PPF as F(X, Y) = 0 which summarizes all Pareto optimal factor allocations (KX, KY, LX, LY) satisfying the optimal conditions of the production side of the economy. MRTSX = MRTSY KX + KY = K LX + LY = L X = f(KX, LX) Y = g(KY, LY) 238 That is, as we said previously in this course, the PPF equation alone is functionally equivalent to the system of five optimal equations that characterize the production side of the economy.
Private Good Y PPF F (X, Y) = 0 Public Good X In terms of production, there is no real difference between public and private goods: both of them require the same capital and labour to be input into the same production processes of the economy. For example, we use the same manufacturing process to produce buses whether they are to transport children to public school (public good) or for private (fee per trip) transportation (i.e. Greyhound). [e] In summary, the model consists of the following components: [i] nonexcludability and joint consumption (nonrivalrous consumption) of public goods (equation (3) below). [ii] excludability and rivalrous consumption of private goods (equation (4) below). [iii] Pareto optimality (equations (1) and (2) below). [iv] and a PPF (equation (5) below) Samuelson's theory of efficient allocation of public goods can now be restated as the following constrained welfare maximization problem: maximize UB (XB, YB) subject to UA (XA, YA) = A 239 (1) (2) XA = XB = X YA + YB = Y F(X, Y) = 0 (3) (4) (5) Theoretically, we can use the calculus techniques of classical optimization to solve this complicated problem of multiple constraint welfare maximization. You will be relieved to know that this is not the route we are going to take. Instead, we will use a simple diagrammatic approach to investigate this problem. [1] First, we describe the production side of the economy by using...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.
 Spring '10
 sning
 Economics

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