derive the expected return beta representation from the equilibrium consumption mode 608397

Formulate the consumption-based model in terms of objective function and budget constraints. Derive the equilibrium asset pricing equation.
Show the equivalence between pricing payoffs and returns.
Derive an expression relating the risk-free rate to the stochastic discount factor. How does the stochastic discount factor influence the risk-free rate?
Derive the expected return-beta representation from the equilibrium consumption model.
Derive the mean-variance efficiency frontier from the equilibrium consumption model.
Show how the stochastic discount factor influences the Sharpe ratio.