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Unformatted text preview: 2011 - Steven Tschantz Choice demand model Steven Tschantz 2/22/11 Problem To determine what firms will charge for products, they need to know how much consumers will buy as a function of prices. Suppose the products of interest are such that consumers will buy just one or not buy at all. How do consumers choose which product to purchase, and whether to purchase at all, in response to prices? How can firms estimate the demands for products? Model Economists think of individuals as acting in their own self-interest, making decisions that maximize the value they perceive. A firm maximizes its profit. But an individual may have preferences between results not simply related to monetary results. Instead, one model imagines individuals behaving as if they had an internal, unobservable measure of the value of each out- come, their "utility" for each outcome, that they maximize over their alternatives. In general, the utility of an individual depends on all of his choices, but often it is simplest to imagine that the utility derived as the result of particular choices can be separated from the utility from other circumstances. More subtle is that the individual's happiness with a result may depend on what other alternatives might have been available. A difficult question is how individuals weigh present costs and rewards against future costs and rewards. Most difficult of all is to evaluate an individual's preference between outcomes that involving a random component, i.e., how individuals evaluate risk. Suppose an individual is choosing which one, if any, of n products to purchase, indexed i = 1, 2, ..., n say, the i-th product offered at price p i . Suppose that when the consumer chooses product i , his utility for that outcome depends only on having chosen that product and the price paid for that product, and does not change if prices for other alternatives are increased. Further suppose that if a consumer would chose a particular product given prices p i , then he would choose the same product if all prices were decreased by the same amount; he would be happier because he pays less, but that extra amount of cash he gets would be the same for each alternative so there should be no reason to change his choice. Imagine there is just one product selling for price p . Below some price, the consumer will choose to buy, while above that price the consumer will prefer not buying at all. This critical price establishes a monetary value the consumer associates to the utility of buying compared to the utility of not buying; the utility of having the product without having the money which is equivalent to having the money without having the product. Let v be this critical price. For a single individual, the demand function is 1 for p < v and 0 for p v . The demand a firm sees is made up of numerous individual choices. Different individuals will have different values. A firm usually cannot effectively charge higher prices to the consumers with higher values, instead assume it will charge the same...
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This document was uploaded on 10/28/2011 for the course MATH 256 at Vanderbilt.
- Spring '11