Lecture 10: Consumption, Saving and Investment I L11200 Introduction to Macroeconomics 2009/10 Reading: Barro Ch.7 16 February 2010

Introduction Last time: – Solved household production decision – Determined equilibrium values wage, capital rent and profit (zero) Today – Begin to solve the household consumption decision – Basic decision is consume now or save for the future?

Last time: Budget Constraint Now solved for right-hand side of this: Profit = 0 Wage to worker w/P* Rent to capital and return on bonds i* Now consider left-hand side

Income Household has an income, given by the wage and rental price of capital This income determines the position of the budget constraint The household has to decide how much to spend vs how much to save, within a budget constraint – Very similar to choosing between goods

‘Intertemporal choice’ Decision about consumption and saving is a decision about consuming today vs tomorrow – Saving today means having more resources available to consume tomorrow – Saving in bonds means more interest income in the future – Saving in capital means more rental income in the future – So this is a ‘now versus later’ choice

Consumption over 2 years In year 1 the budget constraint would be In year 2 the budget constraint would be – Get the time periods right!

Combing 2-year Constraints Both constraints contain term

Combined Constraints We did this so that we can now incorporate the decision about consumption today and tomorrow into one budget constraint which covers two periods Rearranging last equation on previous slide:

Intuition The 2-period budget constraint is intuitive Again, this is just an accounting equation But the /(1+i) terms are important Consumption today + consumption tomorrow = wealth at period 0 + labour income in period 1 + labour income in period 2 – wealth at end of period 2

Discounting Any terms for period 2 are ‘discounted’ at a rate 1+i 1 – This is because period 2 resources are only received later, the cost of the time between period 1 and period 2 is the interest rate – So the value of tomorrow’s income is less because we only receive it tomorrow, and if it were received today it could have earned 1+i interest

Intertemporal Utility To understand how the household will use it’s constrained resources we need utility – Similar to allocating spending between goods: agents equate the marginal utilities – For intertemporal consumption, principle is that households want to smooth consumption – Maintain C 1 equal to C 2 – But the cost of consumption smoothing (saving / borrowing) is the interest rate

Smoothing Consumption 2-period budget constraint Can separate into two components: resources for period 1 & 2 and assets at end of period 2 Assume end of period 2 assets fixed, so can evaluate impact of changing V on C 1 and C 2

Changing Income The impact of increased resources for the household (higher income or initial assets) – Both C 1 and C 2 increase by the same amount – This is known as the ‘income effect’ – Similar to consumption of many goods: higher income increases consumption of both

Changing the interest rate There can also be substitution effects by changing the price of consumption – The price of consumption today vs tomorrow is the interest rate – If the interest rate increases, the price of C 2 decreases. It is more attractive to save – This is known as the intertemporal substitution effect

Changing the Interest Rate Changing the interest rate also has an income effect If i 1 increases: – It raises the return to saving in bonds / cost of borrowing in bonds. Net aggregate effect zero. – It raises the return on capital, so has a positive income effect

Combining the effects So increasing income raises consumption now and in the future – Income spread over periods Effect of raising interest rates is ambiguous – Intertempotal substitution effect encourages saving – But income effect encourages consumption – Net effect could go either way

Summary Modelled household consumption decisions – A ‘now versus the future’ choice – Households aim to keep consumption smooth over time and avoid fluctuations – Implies response to rising income and interest rates differ Next time: final element in the model – How does saving impact investment in capital?