Find the sub game perfect nash equilibrium of this

Question

1. The Concentration Ratio and Herfindahl Index.

The figure below shows the Australian mortgage lending market share in 2007 and 2014:

Australian residential mortgage backed lending change in market share

(a) Compute the N-firm Concentration Ratio, CR(N), for N = 1, 2, 3, and 4 for the Australian residential mortgage market in 2007.

(b) Compute the N-firm Concentration Ratio, CR(N), for N = 1, 2, 3, and 4 for the Australian residential mortgage market in 2014.

(c) Show that the Herfindahl Index for the Australian residential mortgage market in 2007 is between 7.7% and 13.1%.

(d) Show that the Herfindahl Index for the Australian residential mortgage market in 2014 is between 14.8% and 18.3%

(e) The article below provides the sales of new vehicles for major brands in Australia in 2017:

Article  - VFACTS: INDUSTRY CLAIMS ANNUAL RECORD FOR 2017 by Mike Costello

First calculate the 4-firm Concentration Ratio, CR(4), for the Australian motor industry in 2017.

Based on CR(4), determine whether the Australian mortgage market or the Australian motor industry is more concentrated.

2. Product Differentiation and Price Competition: Apple and Samsung.

In many oligopolistic markets, firms offer similar but not exactly the same products (called differentiated products). Examples include products offered by Coles and Woolworths, Coke and Pepsi, Pizza Hut and Dominos, Apple and Samsung, Qantas and Virgin, just to name a few. In this exercise, we study product differentiation and price competition between Apple and Samsung in the market for smartphones.

Assume that the demand for iPhones is determined by the following equation.

Q^A(P A, P S) = 2800 - 2P^A + P^S,

where P A is Apple‘s price for an iPhone, and P S is Samsung‘s price for a Galaxy.

The demand for Samsung Galaxy phones is

Q^S(P A, P S) = 2800 - 2P^S + P^A.

Each firm has a constant marginal cost of $400.

Determine the optimal pricing strategy for each firm.

Calculate the equilibrium profits for each firm.

Consider the following two scenarios independntly

Scenario I. Trump Tariff

Recently the U.S. imposes a 10% tariff on imports of Chinese goods. Suppose the tariff applies to the iPhone. This raise the cost to Apple for the China-assembled smart phones into the United States. Accordingly, the tariff increases the marginal cost of the iPhone by $40. On the other hand, we assume that the tariff has no impacts on Samsung Galaxy, as Samsung makes over half its phones in South Korea and Vietnam.

Redo (a) and (b).

Based on your answers in (a)-(c), discuss how the Trump tariff affects (i) the prices of smartphones, (ii) the market share of each firm, and (iii) the profitability of each firm.

Scenario II. Research and Development

Suppose now each firm can make an investment in R&D to enhance its product features and differentiate the product from its rival. Denote by IA the amount of money Apple spends on R&D, and IS the amount of money Samsung spends on R&D. For simplicity, assume IA and IS admit the following two values: $0 and $100,000. Given (IA, IS), the demand for iPhones is determined by the following equation:

QA(PA; PS; IA; IS)=2800+(IA-IS)/500-2PA+PS

and the demand for Samsung Galaxy phones is

QA(PA; PS; IA; IS)=2800+(IS-IA)/500-2PS+PA

Consider the following two-stage game. In the first stage, Apple and Samsung simultaneously choose R&D spending IA and IS, respectively. In the second stage, after observing each other‘s investment in R&D in the first stage, Apple and Samsung simultaneously choose prices P A and P S, respectively.

Find the sub game perfect Nash equilibrium of this two-stage game.

Based on your answers in (a), (b) and (e), discuss how R&D on product differen- tiation affects (i) the prices of smart phones, (ii) the market share of each firm, and (iii) the profitability of each firm.