NHM 373 Consumer Economics

Microeconomics and BehaviorTest TwoResource Allocation Over Time Notes

Past, Present, and Future Assume we live through time periods t=0,1,2,3,4, Consumption at time t can influence consumption at time t+1, t+2, Expenditures at t Reduced resources at t+1, t+2, Savings at t Increased resources at t+1, t+2, Consumption at time t can be influenced by expectations about time t+1, t+2, Expectation of greater income at t+1 increased resources for consumption at t. Expectation of greater expenditure needs at t+1 Reduced resources for consumption at t.

Consumption Bundles with Two PeriodsIntertemporal Consumption BundlesAlternatives combinations of current and future consumption are represented as points in the C1, C2 plane. By convention, the horizontal axis measures current consumption; the vertical axis, future consumption.Two possible bundles of (C1, C2) D (3000,9000) E (6000,6000)

Consider an Inter-Temporal Decision Suppose your income is $50,000 in the current period and $60,000 in the future period. Assumptions Consumption is allocated to two periods only. Life ends after the second period. No Uncertainty No borrowing constraint At an interest rate of 20%, that is r=0.2 If you deposit $1 in a bank, you can receive $1 plus 20 cents on the future period. Future Value = Principal + Principal*(r) = Principal (1 +r) For every $1.20 you must repay in the future, you can receive $1 now. Present Value = Future Value/(1 +r) Consumers affordability limits can be represented by an inter-temporal budget constraint Two axes: Current period consumption (C1) & Future period consumption (C2) First, you can always merely consume your income in each period. C1=50,000 and C2=60,000 must be a point on the budget constraint Another option is to deposit all $50,000 and thus receive 1.2*50,000 = $60,000 in the next period in addition to the future income $60,000. C1=0 and C2=120,000 is a point on the budget constraint Another option is to borrow 60,000/1.2 = $50,000 in addition to the present income $50,000. C1=100,000 and C2=0 is a point on the budget constraint The Intertemporal Budget ConstraintFor every dollar by which current consumption is reduced, it is possible to increase future consumption by $1.2

The Inter-Temporal Budget ConstraintIntertemporal Budget Constraint with Income in Both Periods, and Borrowing or Lending at the Rate r:The opportunity cost of $1 of present consumption is (1+r) dollars of future consumption. The horizontal intercept of the intertemporal budget constraint is the present value of lifetime income, M1 + M2/(1+ r). M1 M2: Incomes, periods 1 & 2 C1 C2: Consumption, periods 1 & 2 r : interest rate C2m=M1 (1+r) + M2 Maximum resource available in the future period if you set all your current income aside C1m = M1 + M2/(1+r) Maximum resource available in the current period if you dont leave anything for the future period PV (M2)= M2 1+r Present Value of future income This is also your borrowing limit

The Slope of the Inter-Temporal Budget Constraint Slope = -(1+r) It means that a dollars worth of consumption in period 1 can be exchanged for (1+r) dollars worth of consumption in period 2 As the interest rate increases, the steeper the slope gets. It is as if the first period consumption becomes more expensive and second period consumption less expensive.

Exercise Your future income is $110,000 and the interest rate is 10 percent (r=0.10), what would be the present value of your future income? $110,000

Assume your current income is $100,000. Draw the budget constraint.

An Inter-Temporal Indifference MapAs in the atemporal model, movement to the Northeast represents increasing satisfaction. The absolute value of the slope of an indifferent curve at a point is called the marginal rate of time preference (MRTP) at that point. The MRTP at A is I C2/C1l

The Optimal Inter-Temporal AllocationAs in the atemporal model, the optimal intertemporal consumption bundle (bundle A) lies on the highest attainable indifference curve. Here, that occurs at a point of tangency. Saving and Borrowing Negative Saving = Borrowing Saving region in the inter-temporal budget constraint Left of the endowment point Borrowing region in the inter-temporal budget constraint Right of the endowment point

Patience and Impatience(a) The patient consumer postpones the bulk of consumption until the future period. (b) The impatient consumer consumes much more heavily in the current period. But in equilibrium, the marginal rate of time preference (1+r) is the same for both types of consumers. Time Preference and Other Motives for Saving Indifference curves in inter-temporal choice Slope of the indifference curve shows the consumers time preference Neutral Present-oriented: = A steep indifference curve = A high marginal rate of time preference = Impatience = Preference for now over later Future-Oriented: = A flat indifference curve = A low marginal rate of time preference = Patience = Deferment of gratitude

Changes in Interest Rate When interest rate goes up: Inter-temporal budget constraint rotates about the current endowment point Slope of the budget constraint becomes steeper Optimal consumption changes Change toward borrowing less or saving more

Permanent Income Hypothesis: The Effect of a WindfallPermanent Income, Not Current Income, is the Primary Determinant of Current ConsumptionThe effect of a rise in current income (from 120 to 240) will be felt as an increase not only in current consumption (from 80 to 150, but also in future consumption (from 168 to 228). Income in both periods: $120 Interest rate: r=0.2 Consumer receives a windfall of $120 in the current period The effect of a rise in current income (from 120 to 240), with no change in future income, will be felt as an increase not only in current consumption (from 80 to 150), but also in future consumption (from 168 to 228). Why doesnt the consumer spend up the transitory income in the current period? Spreading his windfall over both periods allows him to achieve a better outcome (a higher inter-temporal indifference curve.) The effect of a windfall on current consumption will be even smaller if we consider many future periods. Income and consumption contain a permanent (anticipated and planned) element and a transitory (windfall/ unexpected) element. Any transitory income, either positive or negative, is spread over time. Exercise 1 Karen earns $75,000 in the current period and will earn $75,000 in the future. Assuming that these are the only two periods, and that banks in her country borrow and lend but at an interest rate r=0, draw her inter-temporal budget constraint. Karens Intertemporal budget constraint is C2= 150,000 C1. Her Constraint has endpoint (C1 = 150,000, C2 = 0) and (C1 = 0, C2 = 150,000).

Now suppose banks offer 10 percent interest on funds deposited during the current period, and offer loans at the same rate. Draw her new inter-temporal budget constraint. Her new Intertemporal budget constraint is C2= 157,500 1.1C1. Her new Constraint has endpoint (C1 = 143,182, C2 = 0) and (C1 = 0, C2 = 157,500).

Exercise 2 Kathy earns $55,000 in the current period and will earn $60,000 in the future period. What is the maximum interest rate that would allow her to spend $105,000 in the current period? 20 percent Interest (See Problem 13; Chapter 5) What is the minimum interest rate that would allow her to spend $120,500 in the future period? 10 percent Interest (See Problem 13; Chapter 5)Exercise 3 As the interest rate goes up, an individual becomes:a) More likely to save

The slope of the inter-temporal budget constraint depends on:d) Interest Rate

Inflation and Value of Money http://www.ed.ted.com/lessons/what-gives-a-dollar-bill-its-value-doug- levinson

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