# Demand, Utility, and the Value of Time Today: An introduction to a route choice situation and utility.

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Demand, Utility, and the Value of Time Today: An introduction to a route choice situation and utility

Route choice behavior Two routes Highway Bridge

Travel times 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.

Recall core principle: Equilibrium If you know the route choice of all other people, you can figure out which route is best for you When there are no possible gains by switching routes  equilibrium

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

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

Other issues 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

Core principle: Efficiency Think of the economy as the amount of goods and services available The economy is efficient when economic surplus is greatest Is equilibrium efficient here? This is a later topic

And now, onto bananas Where is our banana eater from Friday? 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 Hypothetical unit of utility: util 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 Friday has the following utility relationship for bananas Banana quantity (bananas/hour) Total utility (utils/hour) 00 170 2120 3150 4160 5150

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 Banana quantity (bananas/hour) Total utility (utils/hour) Marginal utility (utils/banana) 00 70 1 50 2120 30 3150 10 4160 -10 5150

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 Banana quantity (bananas/hour) Total utility (utils/hour) Marginal utility (utils/banana) 00 70 1 50 2120 30 3150 10 4160 -10 5150

Diminishing marginal utility Notice that marginal utility is decreasing as the number of bananas increases Economists typically assume diminishing marginal utility, since this is usually 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 Wednesday

Also for Wednesday Re-read and try to understand the Economic Naturalist examples on p. 136-138 Pay attention to consumer surplus, and how it is calculated

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