We study utility indifference pricing of claim streams with intertemporalconsumption and power (CRRA) utilities. We derive explicit formulasfor the derivatives of the utility indifference price with respect toclaims and wealth. The simple structure of these formulas is a reflectionof surprising operator identities for the derivatives of the optimalconsumption stream. For example, the partial derivative of the optimalconsumption stream with respect to the endowment is always aprojection. Furthermore, it is an orthogonal projection with respect toa natural ”economic inner product”.[...]