1 / 6

Stochastic Demand

Stochastic Demand. Uncertainty in price setting Preferences Competing technologies Income Prices of other goods Weather Sometimes don’t produce enough Reliability issues. Demand. Demand is a function of Price Some random variable, u , that account for uncertainty.

nairi
Download Presentation

Stochastic Demand

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Stochastic Demand • Uncertainty in price setting • Preferences • Competing technologies • Income • Prices of other goods • Weather • Sometimes don’t produce enough • Reliability issues

  2. Demand • Demand is a function of • Price • Some random variable, u, that account for uncertainty. • Distribution of this random variable, f(u), is known by firm • Examine the multiplicative form of Uncertainty • Q=X(p)u • Where X is the mean demand function

  3. Multiplicative Demand • 0<u<∞ • The value of u pivots the demand curve around the vertical axis • E(u)=1 • X(p) is the expected demand curve • Prices is a parameter in the distribution of demand

  4. Expected Value of Welfare • E[W]=E[CS-L]+TR-TC] • L>0 implies excess demand • L=0 otherwise • E[CS]=area under the demand, X(p)u, for all i periods weighted by the probability of, u, occurring. • E[L]=area L weighted by the probability of, u, occurring. • Assumes customers are ranked by WTP, customers with highest WTP are served first, and ranking is costless

  5. Expected Value of Welfare • E[R]=all possible revenue weighted by the, u, possibilities • Broken into parts by excess supply and excess demand • E[C]=all possible costs weighted by the, u, possibilities • Broken into operating costs and capacity costs • Assumes a fixed coefficient technology, with parameters, b, β

  6. Maximize Welfare • Max E[W] • Yields pi=b • Problems with these pricing • When u is large leads to excess demand • Not guaranteed R>C

More Related