problemSolvingHints - A Guide to Problem-Solving for the...

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A Guide to Problem-Solving for the Second Half of EEP/ECON 102 Susan E. Stratton December 3, 2007 We have looked at several different types of problems in the second half of the course. Many of these problems involve multiple steps. These notes are intended as a guide to solving several specific types of problem. They are NOT a comprehensive description of the types of problems you may need to solve. Moreover, these notes focus exclusively on problem solving. You need to be able to explain what’s going on and offer economic intuition for what’s happening as well. 1 Bid-Rent Functions The idea in a bid-rent function problem is that the land owner owns the scarce resource and will therefore extract all the benefits of land at location x . This problem has two basic steps. 1. Determine what profit-maximizing behavior implies about the relationship between q , N , and L . Usually this would be done by solving a profit-maximization problem for a farmer at location x who has agreed to rent land at price of r ( x ) . In the example in your problem set, it will require thinking a little about profit-maximizing behavior because you can’t use calculus to solve the problem. Try drawing several isoquants for specific levels of output if you get stuck on this problem. 2. Once you’ve found the profit-maximizing relationships, solve for the rent function r ( x ) which sets total profits to 0. You can get this by solving ( p - cx ) q = wN + r ( x ) L for r ( x ) . The left hand side is total revenue and the right hand side is total cost. If they’re equal, profits are 0. Therefore, r ( x ) = ( p - cx ) q L + w N L . The lecture notes define two quantities – a N ( x ) = q N and a L ( x ) = q L . This allows us to rewrite the zero-profit condition as r ( x ) = ( p - cx ) a L ( x ) + w a L ( x ) a N ( x ) .
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