Demand, Utility, and the Value of Time

Demand, Utility, and the Value of Time Today: A route-choice activity, and an introduction to utility

Second: An activity • Form groups of three or four people • Each group represents a carpool • If you are not in a group of three or four people, please raise your hand and Rosemarie or I will find a group for you • Your carpool will represent one of N cars on the road • 4 rounds of choosing routes

Your task • Choose between a highway and a bridge in each of the 4 rounds

More information on your task • Travel time on the highway is 20 minutes, no matter how many other cars travel on this route • The bridge is narrow, and so travel time is dependent on the number of other cars on the bridge • If 1 car is on the bridge, travel time is 10 minutes; 2 cars, 11 minutes; 3 cars, 12 minutes; etc.

Your extra credit grade will have 3 components Attendance here today Total travel time A set of questions on the first page You may talk with other people in your carpool about which choice you want to make You are not allowed to talk to anyone outside of your carpool Remember: This is extra credit

What happened? • Assume someone is rational if he/she has a positive value of time • A rational person would likely decide to travel the bridge if bridge time < 20 minutes • Travel the HW if bridge time > 20 minutes • Notice that the same decision rules above apply to each car • Supply is determined by constraints on bridge

What happened? minutes S D 20 # of cars on bridge 11 N

Other issues with this traffic network • In real commuting situations, some people have higher values of time than others • Suppose we charge a toll on the bridge • New equilibrium: Bridge time < 20 min. • Why? Think both time and money as costs • Who travels on bridge now? People with high values of time, since they look at the toll as a relative bargain • Is “no toll” or “toll” best? This is a later topic

And now, onto bananas • Where is our banana eater from Wed.? • How many did you eat? • Your bananas were “free,” right? • Why did you not eat more than you did?

Bananas and utility • A fundamental concept in economics is utility • Think of utility as a level of satisfaction (similar to total benefit) • The higher your utility, the more satisfied you are

Bananas and utility • Suppose our volunteer from Wednesday has the following utility relationship for bananas

Marginal utility • Marginal utility (MU) tells us how much additional utility gained when we consume one more unit of the good

Marginal utility of bananas

If P = $0, maximize utility • Utility is maximized when 4 bananas are eaten • When P ≠ $0, we need a way to maximize utility given a budget • We can easily maximize utility if we have diminishing marginal utility

Diminishing marginal utility • Notice that marginal utility is decreasing as the number of bananas increases • Economists typically assume diminishing marginal utility, since this is consistent with actual behavior

Diminishing marginal utility and the rational spending rule • If diminishing marginal utility is true, we can derive a rational spending rule • The rational spending rule: The marginal utility of the last dollar spent for each good is equal • Exceptions exist when goods are indivisible (we will ignore this for now)

The rational spending rule • Why is the rational spending rule true with diminishing marginal utility? • Suppose that the rational spending rule is not true • We will show that utility can be increased when the rational spending rule does not hold true

The rational spending rule • Suppose the MU per dollar spent was higher for good A than for good B • I can spend one more dollar on good A and one less dollar on good B • Since MU per dollar spent is higher for good A than for good B, total utility must increase • Thus, with diminishing MU, any total purchases that are not consistent with the rational spending rule cannot maximize utility

The rational spending rule • The rational spending rule helps us derive an individual’s demand for a good • Example: Apples • Suppose the price of apples goes up • Without changing spending, this person’s MU per dollar spent for apples goes down • To re-optimize, the number of apples purchased must go down • Thus, as price goes up, quantity demanded decreases

Individual demand • Now that we have derived that individual demand is downward sloping, how do we get market demand? • Keep reading Chapter 5 and you can find out… • …or you can wait until Monday

Demand, Utility, and the Value of Time