Question

"Find the general form of the state prices for a representative agent with the following utility function:

U(C^0, C^s) = (1-r)C^0^(1-r) + (1-r)e^(-δ)(C^s - βC^0)^(1-r)

Given that C^0 is consumption at date 0 and C^s is consumption at date 1 contingent on state s occurring

Answer 1

The state prices for a representative agent can be found by taking the partial derivatives of the utility function with respect to each consumption variable.

Step-by-step explanation:

The general form of state prices for a representative agent with the given utility function can be found by taking the partial derivatives of the utility function with respect to each consumption variable. In this case, we have:

State price for date 0 consumption (C^0): (1 - r)C^0^(-r)

State price for date 1 consumption (C^s): (1 - r)e^(-δ)(C^s - βC^0)^(-r)

Where r is the coefficient of relative risk aversion, δ is the discount rate, and β is the parameter that determines the intertemporal elasticity of substitution.