9. Consider a simple two-period model of a consumer's intertemporal consumption decision problem. The consumer faces the

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9 Consider A Simple Two Period Model Of A Consumer S Intertemporal Consumption Decision Problem The Consumer Faces The 1 (41.28 KiB) Viewed 39 times

9. Consider a simple two-period model of a consumer's intertemporal consumption decision problem. The consumer faces the following utility function with regards to consumption today. G. and consumption tomorrow.cz UG.cz) - Inc + Bing where B € (0.1) defines consumer's (subjective) discount factor. Their intertemporal budget constraint can be written as: 1+ wherer > 0 is a market (real) interest rate, in which the consumer can lend/borrow freely, and Y > defines the consumer's total wealth in both periods known at the beginning of period 1. The consumer lives only for two periods, and leaves no debtinheritance behind (a) State formally the maximisation problem for this consumer and define the Lagrangian function. (5 marks) (b) Derive the first order conditions of this problem and solve for optimal consumption at both periods. (5 marks) (c) Check the second-order sufficient condition for a maximum using the bordered Hessian determinant. (5 marks) (d) Compute the maximum utility (value) function the consumer obtains, gathering terms in the log of consumer's total wealth, Y. (5 marks) EC206 2021/2 A 800 Turn over Page 6 (e) Provide a comparative static analysis for the equilibrium solutions of consumption in both periods with respect to all the exogenous variables and parameters of this model. (6 marks) (1) Verify that the first derivative of the maximum utility (value) function with respect to total wealth, Y, is equal to the Lagrange multiplier, 1 (4 marks)