Lecture02-2003 - Lecture II: Applications of Mathematical...

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Lecture II: Applications of Mathematical Programming in Agricultural Economics I. Interregional and Spatial Economics A. A large section of the literature, but I only want to discuss two types: 1. Arbitrage or regional supply and demand models. If demand were distributed identically across all areas of the country, but there was a primary supply region (for example the orange juice market). What would the equilibrium look like? What is the impact of profit on a change in transportation costs? What happens if Brazil enters the market? 2. Plant location models. In the past most heavy industry was located in the north, particularly in the area around the great lakes. As the population shifted south more industry shifted south. Why? Current topics, the technology is being developed to condense most of the water out of milk, reducing its shipping cost. Will this cause the dairies to move to Wisconsin? If you were John Deere how do you determine where to locate your warehouses? B. Leibnitz’s Rule () ( ) () ( ) , , ,, Br Ar Vr fxrd x fxr fBrr fA rr d x r r = ∂∂ == + 1. In a market equilibrium () () 00 max xx ds x p zd z z ∫∫ a. d p z is the consumer’s inverse demand curve and s p z is the producer’s supply curve. b. This amounts to maximizing the sum of consumer surplus and producer surplus. a. Differentiating the sum of consumer surplus and producer surplus yields ( ) ( ) 0 pz pz = b. Extending the problem
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AEB 6533–Static and Dynamic Optimization Lecture 2 Professor Charles B. Moss 2 () () () () ( ) 12 1 ,, 000 11 1 2 1 22 2 max .. 0 0 T T xxx dds T ds p zd z z z t x st x x x S px px x x S px px x t x + −− +≤ ⇒= += =− + = ∫∫∫ II. Econometrics and Statistical Applications A. Historically, econometrics relied on closed form solutions made possible by linear models of normally distributed random variables.
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Lecture02-2003 - Lecture II: Applications of Mathematical...

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