ion # 1 (10+5+5 = 20 points) Consider a 2 -period model with credit constraints: Let preferences of the representative consumer be described by the utility function "1 ( 9 , C 2 ) = Va + Bucz, where c, denotes consumption in period one and c, denotes consumption in period two. The parameter B is known as the subjective discount factor and measures the consumer's degree of impatience in the sense that the smaller is B, the higher the weight the consumer assigns to present consumption relative to future consumption. Assume that B=1/1.1. For this particular utility specification, the marginal utility functions are given by ", (C, (2) = 1 and 12 ( 9 , (2 ) = = B 2 Na 2 J C 2 The representative household has initial real financial wealth (including interest) of do =1 The household earns y, = 5 units of goods in period one and y2 = 10 units in period two. The real interest rate paid on assets held from period one to period two equals 10% (i.e., 1 = 0.1). a. Calculate the equilibrium levels of consumption in periods one and two. (Hint: Set up the Lagrangian and solve.) b. Suppose now that lenders to this consumer impose credit constraints on the consumer. Specifically, they impose the tightest possible credit constraint - the consumer is not allowed to be in debt at the end of period one, which implies that the consumer's real wealth at the end of period one must be nonnegative (a, 2 0) (Note: here, a, is defined as being exclusive of interest, in contrast to the definition of a, above). What is the consumer's choice of period-one and period- two consumption under this credit constraint? Briefly explain, either logically or graphically or both. C. Does the credit constraint described in part b enhance or diminish welfare (i.e., does it increase or decrease lifetime utility)? Specifically, find the level of utility under the credit constraint and compare it to the level of utility obtained under no credit constraint