Lecture 10: Consumption, Saving and Investment I

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

2. 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?

3. 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

4. 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

5. ‘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

6. 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!

7. Combing 2-year Constraints • Both constraints contain term

8. 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:

9. 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

10. Discounting • Any terms for period 2 are ‘discounted’ at a rate 1+i1 • 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

11. 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 C1 equal to C2 • But the cost of consumption smoothing (saving / borrowing) is the interest rate

12. 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 C1 and C2

13. Changing Income • The impact of increased resources for the household (higher income or initial assets) • Both C1 and C2 increase by the same amount • This is known as the ‘income effect’ • Similar to consumption of many goods: higher income increases consumption of both

14. 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 C2 decreases. It is more attractive to save • This is known as the intertemporal substitution effect

15. Changing the Interest Rate • Changing the interest rate also has an income effect • If i1 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

16. 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

17. 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?