please solve the following in detalis

3. True or False: An implication of the Hansen indivisible labor RBC model is that consumption and labor productivity will have the same time series properties. 4. Consider an exchange economy populated by identical agents that trade equity shares, z, defined as title to the endowment process. (That is, this is the same asset priced in the Lucas tree model.) Denote the price of equity as qr. Agents also trade one-period bonds which cost p units of consumption in period t and return 1 unit of consumption in the following period. In addition to these assets, a one-period forward contract on bonds is traded. In this contract, agents agree at time t to pay o, units of consumption in period # + 1 for the promise of one unit of consumption to be received in period +2. The endowment, It, is stochastic and varies over the interval (2, F); furthermore, z, is assumed to be independently and identically distributed. Given this environment, agents choose a sequence of consumption and assets in order to maximize Fo EAU (C) (a) Formulate the agent's problem as a dynamic programming problem. Be explicit in identifying the state and control variables. (b) Derive and interpret the necessary conditions which characterize the solution to this maximization problem. (e) Define a recursive competitive equilibrium in this economy. (d) Prove that equilibrium bond and equity prices are positively corre- lated with the endowment while the price of the forward .- constant. Explain these results.7. Consider a representative agent, exchange economy similar to that studied by Mehra and Prescott. Specifically, it is assumed that the endowment, It, grows stochastically as given by 1 = Art1I, where the growth rate, At,is assumed to be independently and identically distributed. Agents maximize lifetime expected utility: Eo [ & [ ce - he-1)'- where Be (0, 1) and 0 0 affect the volatility of bond prices? Discuss the implications that these results have for the assumption of habit persistence to help resolve some asset pricing puzzles