Monday, October 29, 2018

Platforms as Market-makers


There are two different ways of looking at markets: metaphorically and as "platforms."  Metaphorically, markets are ways of characterizing transactions between a group of buyers and sellers for a given product, in a geographic location, and during a specific time.  There is no literal marketplace, but prices and quantities behave as if there were.  

Platforms are literal markets that are under the control of a market maker, like Uber, who can set different prices to buyers (riders) and sellers (drivers).  For example, suppose that there were seven sellers with marginal costs {$1,$2,$3,$4,$5,$6,$7} and seven buyers with values={$7,$6,$5,$4,$3,$2,$1}.  Uber makes money on the spread between what it receives from riders and what it pays to drivers.  With these supply and demand curves, we show Uber
s profit calculus below.

Margin
Quantity
Profit
(7-1)=6
1
6
(6-2)=4
2
8
(5-3)=2
3
6
(4-4)=0
4
0

·       If Uber paid $1 and sold at $7, it would sell one ride for a profit of $6. 
·       If Uber paid $2 and sold at $6, it would sell two rides for a profit of $8. 
·       If Uber paid $3 and sold at $5, it would sell three rides for a profit of $6. 
·       If Uber paid $4 and sold at $4, it would sell four rides for a profit of $0. 

The profit maximizing prices are in red above.  The table also shows how the competitive equilibrium (a single price) is actually a special case of the platform with zero margin. 

This raises an interesting question, is it ever profitable to bring an extra driver into the market?  In this simple example, the answer is no.

However, the answer changes if bringing more drivers into the market increases the riders value for rides by reducing the waiting time.    For example, suppose that an extra unmatched driver into the market reduces waiting time by enough so that it increases the willingness to pay by every rider by $2, i.e., with values={$9,$8,$7,$6,$5,$4,$3}.  This would change the profit calculus as follows:

Margin
Drivers
Riders
Profit
(9-2)=7
2
1
7
(8-3)=5
3
2
10
(7-4)=3
4
3
9
(6-5)=1
5
4
4

·       If Uber paid $2 and sold at $9, it would sell one ride for a profit of $7. 
·       If Uber paid $3 and sold at $8, it would sell two rides for a profit of $10. 
·       If Uber paid $4 and sold at $7, it would sell three rides for a profit of $9. 
·       If Uber paid $5 and sold at $6, it would sell four rides for a profit of $4. 

With an extra unmatched driver, the margin that Uber can charge increases by $2, which is enough to offset the cost of bringing an extra driver into the market.  In fact, these kind of network effects work in both directions.  Just as bringing more drivers into the market reduces the waiting time for riders (increasing demand), so too does bringing more riders onto the platform make it easier for drivers to find nearby riders (increasing supply). 

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