© 2011  Steven Tschantz
Notes on modeling
Steven Tschantz
3/31/11
Summary
We have had nearly ten weeks of lectures and labs illustrating specification and implementation of mathematical models in
economics. Next we will have a test of your knowledge and proficiency with regards to the following.
1. Demand models.
We have imagined consumer demand for a single product as a function of its price or for several (differentiated) products as
functions of their prices. We have considered linear, constant elasticity, and logit demand forms, calibrating demand functions
to a variety of given data. You need to know the definitions of own and crossprice elasticity of demand.
2. Firm model.
We have often supposed that one or a few firms sell to a large population of consumers, and that firms are price setters and
consumers are price takers, with consumers unable to negotiate and firms unable to price discriminate. The profit a firm makes
is a function of the price it charges for its products, the sales of those products as determined by the demand of the consumers,
and the costs incurred in producing and selling that quantity of goods. The firm is assumed to be profit maximizing. You need
to know the definition of marginal cost.
3. Competition.
We have argued that when firms compete they set price to maximize their own profits assuming their competitors prices are
given. This defines equilibrium conditions for prices which are best for each firm separately, given the prices of the other firms.
If firms cooperate or merge, then the prices which maximize their total profits will be different. You need to be able to write
down equilibrium conditions, and solve for equilibrium prices. You need to know the definition of passthrough rate.
4. Other market models.
We have considered also a model where many producers sell identical goods to many consumers, describing the willingness to
sell and buy by supply and demand functions, and imagining a single market clearing price. We have considered a model
where a manufacturer sets wholesale price to retailers, each retailer setting price to their local consumers, comparing this to a
vertically integrated firm. Given the organization of a market, the available actions of the players in that market, and the
objectives of those players, we evaluate which actions best meet each players own objectives in competition with the others.
By varying the assumptions and parameters of such a model we hope to better understand how real markets work.
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5. Estimation.
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 Spring '11
 Schantz
 Math, Supply And Demand, p1

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