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Recently several cities in the US, including New York, San Francisco, Seattle and Washington, D.C., imposed a temporary cap of 15% on commission charged by third-party delivery platforms. Suppose the Australian government is also considering to impose a 15% cap on commission charged by third-party delivery platforms. Based on your answers in (e), discuss how this government intervention will a§ect (i) the proÖts of Menulog and Uber Eats, and (ii) the number of restaurant signups to each platform. Do you think the government should intervene to see restaurants through the pandemic? Justify your answer

Article https://www.sltrib.com/news/2020/07/19/delivery-fees-double/

Answer (e)

a. Revenue function:

 

 - Uber Eats: 200 x 20 x Cu x Nu

 - Menulog: 200 x 20 x Cm x Nm

 

Cost function:

 

 - Uber Eats: 2 x 200 x Nu = 400 x Nu

 - Menulog: 2 x 200 x Nm = 400 x Nm

 

Profit function:

 

 - Uber Eats: (4,000Cu - 400) x (100 - 224Cu + 40Cm)

 - Menulog: (4,000Cm - 400) x (100 - 224Cm + 40Cu)

 

b. The data in the table below can be obtained by substituting the data into the formula obtained in a.

 

 

 

 

 


35%

30%

25%

35%

35600,35600

33600,37440

31600,34800

30%

37440,33600

35840,35840

34240,33600

25%

34800,31600

33600,34240

32400,32400

 

 

Regardless of what decisions Menulog make, Uber Eats will only either 35% or 25% with the maximized average profit of $33,600. Menulog will also do so. If both select 35%, both profits are $35,600. If Uber Eats selects 25% and Menulog selects 35%, their profits are $34,800 and $31,600. If Uber Eats selects 35 and Menulog selects 25%, their profits are 31,600 and 34,800. If both select 25%, both profits are $32,400. Therefore, this time, there are 4 Nash equilibriums (35%; 35%), (25%; 25%), (35%; 25%), (25%; 35%)

 

(35%; 35%) => Profit ($35,600; $35,600) => Revenue ($49,840; $49,840) => Market share (50%; 50%) => Herfindahl Index (HHI) = 50^2 + 50^2 = 5,000

 

(25%; 25%) => Profit ($32,400; $32,400) => Revenue ($54,000; $54,000) => Market share (50%; 50%) => Herfindahl Index (HHI) = 50^2 + 50^2 = 5,000

 

(35%; 25%) => Profit ($31,600; $34,800) => Revenue ($44,240; $58,000) => Market share (43.27%; 56.73%) => Herfindahl Index (HHI) = 43.27^2 + 56.73^2 = 5,090.57

 

(25%; 35%) => Profit ($34,800; $31,600) => Revenue ($58,000; $44,240) => Market share (56.73%; 43.27%) => Herfindahl Index (HHI) = 56.73^2 + 43.27^2 = 5,090.57

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