A free theater ticket can still be too expensive. You might turn it down because your evening has value. That familiar fact has a less familiar implication: a high markup on the ticket need not mean a high markup on the night out.
When the price changes, people adjust. There are many margins of adjustment. The standard model assumes adjustment just by buying or selling less, just about quantity. But they can also change quality, wait longer, or buy different bundles. Half of price theory is asking what else can adjust when prices change.
(the ratio of a product’s price to its marginal cost) and call that a measure of market power. But interpreting that ratio requires accounting for the customer’s time, not just the firm’s costs. A paper with Thomas Phelan and Nick Pretnar, recently published in the Journal of Economic Theory, works out how time changes both firms’ markups and the incentives to create new products
Deriving demand from “experiences”
Gary Becker’s insight was to treat households as producers of the experiences they want. The thing you buy (say, a theater ticket) is one input into a household production function. You combine it with your own time to produce the thing you ultimately care about, an evening watching a show. You can think of the theater ticket as an ingredient and the production function as a recipe, as we’ve written about before.
In this framing, demand for the theater ticket is derived demand, similar to how a firm’s demand for labor is derived from what it can produce. You can decompose that demand into two parts: a scale effect and a substitution effect. If you raise the ingredient’s price, you do less of the activity. That’s the scale effect. If the recipe allows it, you also use less of the ingredient in each unit that you produce, putting in more of your own time per unit. That’s the substitution effect.
These are the same two effects behind Hicks-Marshall’s laws of derived demand, as we discussed with labor demand and AI. There the price that fell was AI’s, the input in question was labor, and the two effects pulled against each other: cheaper AI means more output and more work to do, but less labor in each unit of output.
You are not a horse
There’s a popular argument that AI will do to human workers what tractors did to horses. Tractors could do what horses did. Horses became obsolete. AI can do what humans do. Therefore...
Here the price that moves is the ingredient’s own, so both effects cut purchases. It’s a different horse race (terrible pun) between two effects but a different comparative static.
The meaning of markups when time matters
Before we think about margins of adjustment, let’s do some basic accounting and assume that the recipe is fixed.
This is the theater example. An extra hour in your seat doesn’t replace part of the ticket. A night at the theater takes one ticket and three hours.
Take two theaters offering different shows to the same customers, who value their time at $100 per evening out. One has a marginal cost of $20 a seat and charges $50. The other’s marginal cost is $4 and it charges $30. Price over marginal cost is 2.5 at the first theater and 7.5 at the second. That ratio is the usual markup, but it leaves out most of what the customers pay for their evening.
Each theater is going to price based on the demand curve it faces. Suppose attendance at either theater falls by about 5 percent for each 1 percent rise in the full cost of its evening out.
Let’s think of the second theater. The ticket is $30 against $100 of time, so raising the ticket price 1 percent raises the cost of an evening about 0.23 percent. That cuts ticket sales by about 1.15 percent. Demand for evenings is elastic and demand for its ticket is much less elastic, because the ticket is a small part of the evening.
The first theater’s ticket is a third of the evening, so the same 1 percent ticket-price rise costs it about 1.67 percent of its sales. Those demand elasticities give us the profit-maximizing ticket markups of 2.5 and 7.5, respectively. The second theater can charge a higher multiple of its marginal cost because customers are less responsive to percentage changes in its ticket price.
A dollar added to the ticket is a dollar added to the evening, and the time the evening takes doesn’t change, so in this fixed proportions case, it is like the firm is pricing the full experience. On the evening, both have the same “holistic markup,” as we call it. This is the full price of the experience over its full marginal resource cost: $150 over $120, and $130 over $104. Both are 1.25.1
This gap is not peculiar to these numbers. The usual markup in our model is always at least as large as the holistic one. With a positive markup and valuable consumption time, it is strictly larger—even with a fixed recipe
With a fixed recipe, this economy is equivalent to the textbook constant-elasticity model of differentiated products, with the full resource cost of a night out in place of a firm’s marginal cost. That model, with free entry, is efficient under the paper’s assumptions. This is Dixit-Stiglitz. The allocation in that model is efficient while measured markups differ by a factor of three. Dispersion in ticket markups does not by itself show that something has gone wrong.
Adjusting your time use
Now let’s imagine it is something where you can change how much time you allocate. Think of video games. (Let me know if you have a better example; I don’t love this one but its okay.) As prices rise, you can spend more time playing each one.
Raise the price and people consume less of the gaming experience. That is the scale effect. They can also buy fewer games and spend longer on each one to get a given amount of enjoyment. That is substitution.
With a fixed recipe, every lost ticket sale is a lost evening. With games, some of the lost sales come from people who are still gaming. They just replay more and buy less. We’ve seen a related distinction before: retirees can spend less on food without eating less, because they spend more time shopping and cooking.
That makes the game seller’s demand more elastic than the scale effect alone would imply. Keeping the experience-demand elasticity at 5, its holistic markup falls below 1.25. How far below depends on both the ease of substituting time for purchases and the purchase’s share of the full price of the experience.
Time therefore does two different things. It makes the purchase price a smaller part of the full cost. But it can also give customers another way to economize on purchases, another margin of adjustment. A small purchase share weakens the scale effect but it does not make the substitution effect disappear.
Do we get enough new products?
The paper closes this demand equation in a whole model with firm entry and other bells and whistles. So we can ask, does enough effort go into creating new products?
Usual markups are what pay for new products. Markups allow them to make profits to justify entering. Firms enter until profits cover the cost of starting up.
The question is whether the amount of entry that results is efficient. With a fixed recipe the answer is yes: the economy is equivalent to the standard model of differentiated products, and free entry gets the right number of them. When the recipe can change, every holistic markup falls below the fixed-recipe level, profits fall with it, and too few products get created.
The markup on purchases, but not on customers’ own time, pushes them toward a more time-intensive recipe than resource costs justify.
The paper also breaks the usual inference from markups to efficiency. We build two different consumer problems that produce the same demand curve for a product but imply an efficient allocation in one case and an inefficient allocation in the other. Different measured markups can coexist with an efficient allocation. Identical measured markups can coexist with an inefficient one. Even a perfectly measured markup is a residual that needs an explanation.
Measured markups systematically overstate the markup on the full experience, and the gap can be especially large for products where the customer's time is most of the cost.
Time is just one of those margins that adjusts when a price moves. I think it’s an important one.
I've argued before that markups are too low to get the right amount of product creation. Time use makes the problem worse and changes which firms it hits hardest. A high measured markup usually looks like a firm with too much market power. Here it can mean the product is a small share of the experience, the holistic markup is low, and the gap between measured and holistic is wide. The firms with the highest measured markups are the ones whose reward for creating products falls furthest short.
With demand for attendance x = A(p + t)^(−η), the theater maximizes (p − k)x, which gives p − k = (p + t)/η, or p = (ηk + t)/(η − 1). With η = 5 and t = $100 that is p = 1.25k + 25. Full price over full resource cost is then η/(η − 1) = 1.25 whatever the ticket’s marginal cost k happens to be.