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