@K.R.Bhattarai, Business School, University of Hull, UK. 1 Economic Modelling Lecture 4 Optimal Consumption (Micro foundation)

@K.R.Bhattarai, Business School, University of Hull, UK. 2 Two Period Model of Consumption Consumers problem: = subjective Discount factors : Consumption in period 1 : Income in period 1 :Income in period 12 b = borrowing or lending r = interest rate U = utility Budget constraint in period 1: Budget constraint in period 2:

@K.R.Bhattarai, Business School, University of Hull, UK. 3 C1 C2 w1 c1 c2 w2 Two Period Model of Consumption and Saving Borrowing Subject to: U U

@K.R.Bhattarai, Business School, University of Hull, UK. 4 First Order Conditions of Consumers Optimisation A Lagrangian function for constrained maximisation problem: shadow value of income in terms of utility First Order Conditions of Optimisation:

@K.R.Bhattarai, Business School, University of Hull, UK. 5 Marginal Rate of Substitution Between Current and Future Consumption When r =0 and =1 When Consumer values current and future equally and the interest rate is zero Consumption in all periods is equal.

@K.R.Bhattarai, Business School, University of Hull, UK. 6 Optimal Saving and Consumption in Two Period Model 100 =100 r = 0.05 Intertemporal budget constraint: Optimal consumptions =0.95 Current Consumption is more expensive at higher interest rate of 10 percent:

@K.R.Bhattarai, Business School, University of Hull, UK. 7 Results of Two Period Optimisation Model Lower the subjective discount rate, higher will be consumption today and lower will be consumption tomorrow. Higher interest rate makes current consumption more expensive compared to future consumption. People tend to save to consume more tomorrow. Lower interest makes current consumption cheaper. People borrow, spend and consume more today. Consumption will be higher for higher the level of wealth.

@K.R.Bhattarai, Business School, University of Hull, UK. 8 C-Smoothing YoungAdult Old Saving Borrowing Dissaving C,S,Y Life Cycle Model of Consumption and Saving Modigiani-Ando-Brumberg life cycle hypothesis Smooth consumption and erratic income over life

@K.R.Bhattarai, Business School, University of Hull, UK. 9 What is the optimal consumption in each period if Subject to: Optimal Consumption-Saving Model while Young, Adult and Old

@K.R.Bhattarai, Business School, University of Hull, UK. 10 Four Optimisation Conditions

@K.R.Bhattarai, Business School, University of Hull, UK. 11 Consumption and Savings in Three Periods

@K.R.Bhattarai, Business School, University of Hull, UK. 12 References Blanchard (3,16) Caballero Ricardo J. (1991), ``Earning Uncertainty and Aggregate Wealth Accumulation", American Economic Review. vo. 81, no. 4, Goodman Alissa and Webb Steven (1994) "For Richer, For Poorer: The Changing Distribution of Income in the UK, ", Fiscal Studies, vol. 15 no.4, pp Jenkins Stephen P. (1996)"Recent Trends in the UK Income Distribution: What Happened and Why?" Oxford Review of Economic Policy, Vol; 12, No. 1. Kimball Miles S. and N. G. Mankiw (1989) " Precautionary Saving and Timing of Taxes" Journal of Political Economy vol. 97, no. 4 pp Modigliani F (1986) Life cycle, individual thrift and the wealth of nations, American Economic Review 76, Pemberton James (1997), ``The Empirical Failure of the Life Cycle Model with Perfect Capital Markets", Oxford Economic Papers. vol. 49, pp