Comprehending Economic Principles: Elasticity, Investment Risk, and Market Structure Analysis

Objective of PART 1 - Comprehending Essential Economic Principles and Determinants Influencing Elasticity

The objective of PART 1 of this assignment is to facilitate students' comprehension of essential economic concepts, including anticipated returns, profits, and pricing, and to apply their knowledge of the determinants influencing the elasticity of demand and supply for products and services.

1. Two investments possess the following anticipated returns (net present values) and standard deviations of returns.

Which option presents a greater risk? Provide a rationale for your response.     

The AIROD Aircraft Company manufactures tiny, recreational aircraft. Historical data indicates that sales volume is influenced by fluctuations in aircraft pricing and the economic condition, as assessed by customers' disposable personal income. The accompanying data on the sales, selling prices, and customers' personal income of AIROD Aircraft Company was gathered:

1. Calculate the arc price elasticity of demand using the data from 2013 and 2014.
2. Calculate the arc income elasticity of demand using the data from 2013 and 2014.
3. Assuming these projections would stay unchanged throughout 2015. Project 2015 figures for AIROD Aircraft Company, supposing that aircraft prices stay unchanged from 2014 and that disposable personal income would rise by RM40 billion. Furthermore, consider that the arc income elasticity calculated in (b) above is the most accurate estimate of income elasticity available.
4. Project the 2015 sales for AIROD Aircraft Company, considering an increase of RM20 in aircraft pricing from 2014 and a rise of RM40 billion in disposable personal income. Assume that the effects of price and income are independent and additive, and that the arc income and price elasticities calculated in sections (a) and (b) represent the most accurate estimates for forecasting purposes. 

The objective of PART 2 of this assignment is to refine students' analytical abilities regarding production functions, cost minimization, and profit maximization, while also recognizing their practical applications in the actual world.

1. Table 1 below presents data on Gross Domestic Product (GDP), labor, and real capital for Mexico from 1955 to 1974.

Table 1: Real GDP, Labor, and Real Capital for Mexico from 1955 to 1974

1. Construct a regression equation using GDP as the dependent variable and Labor and Capital as the independent variables. Utilize logarithms for all variables.     
2. Construct a regression equation using GDP per labor as the dependent variable and GDP per capital as the independent variable. Utilize logarithms for all variables.
3. Assess if this production function demonstrates growing, decreasing, or constant returns to scale, and illustrate using an appropriate illustration.

PART 3 of this assignment aims to assist students in assessing competitiveness within different market structures and to provide appropriate methods for achieving a competitive advantage in a chosen market.

1. Michael Porter established a conceptual framework for recognizing competitive advantage via five dynamics of competition within a relevant market. Utilizing an appropriate illustration, provide a critical explanation of Porter’s Five Forces Strategic Framework.
2. Alchem (L) is a pricing leader in the polyglue sector. All ten other manufacturers (follower [F] enterprises) provide polyglue at the same price as Alchem. Alchem permits other enterprises to sell unlimited quantities at the established price and fulfills the remaining demand independently. The overall demand for polyglue is represented by the equation (QT = QL + QF):

P = 10,000 - 10QT

Alchem's marginal cost function for the production and sale of polyglue is:

MCL = 100 + 3QL

The cumulative marginal cost function for the remaining polyglue producers is:

∑MCF = 50 + 2QF

1. To optimize earnings, what quantity of polyglue should Alchem manufacture, and what price should it set?
2. What is the aggregate market demand for polyglue at the price set by Alchem in Part (a)? What proportion of overall demand is supplied by the following firms?

PART 4 of this assignment aims to ensure that students can use their understanding of market theories to evaluate contemporary developments in the competitive landscape.

The leading makers of affordable random access memory chips, an essential element in all consumer electronic products, consented to penalties and incarceration for numerous executives due to price fixing from 1999 to 2002. The criminal conspiracy increased costs by 400 percent over six months, from US$1 to US$4 per 100 megabits, then thereafter coordinated to sustain the price at US$3.

DRAM chips are standardized and readily interchangeable across providers. Consequently, a CARTEL agreement to restrict output is essential to maintain prices above competitive thresholds. SAMSUNG and HYNIX, two South Korean companies that manufacture the majority of chips, incurred penalties of US$300 million and US$185 million, respectively. Infineon Technologies of Germany paid a punishment of US$160 million, and four executives were incarcerated for many months, each paying individual penalties of US$250,000. Micron Technology, located in Boise, Idaho, was granted immunity for its collaboration with prosecutors and complainants DELL and HP in building the case. 

Source: Derived from "SAMSUNG to pay," Wall Street Journal (October 14, 2005), p. 43, and "Hynix Pleads Guilty," Wall Street Journal (April 22, 2004), p. 86. 

Kindly peruse the aforementioned content and respond to the subsequent questions.

1. Utilize an appropriate diagram to elucidate the price-output determination for a two-firm cartel's profit maximization and the distribution of constrained production, respectively. 
2. Assume that two South Korean electronics firms, Samsung (Firm S) and Hynix (Firm T), together own a patent for a component used in DRAM. The demand for the component is represented by the following function:

P = 1,000 - Q_S - Q_T

Where QS and QT represent the amounts sold by the individual businesses, and P denotes the market selling price. The total cost functions for the production and sale of the component for the individual enterprises are:

TCs = 70,000 + 5QS + 0.25Q²S

TCt = 110,000 + 5QT + 0.15Q²T

• Assume that the two enterprises operate independently; ascertain the optimum production and pricing, with each company aiming to maximize its overall profit from component sales.
• Assume that the two enterprises choose to establish a cartel and operate as a monopolist to optimize overall earnings from the manufacturing and sale of components. Ascertain the optimum production, market share, and overall profit of the firm in the event of a cartel formation.  

Objective of PART 1 - Comprehending Essential Economic Principles and Determinants Influencing Elasticity

A market system in which producers collaborate to establish individual and collective production levels and prices is referred to as a cartel. In a perfect cartel scenario, the production and pricing of the whole industry, along with each member business, are dictated by a central authority, facilitating the realization of collective profits for the individual enterprises. The ensuing profit is allocated according to a predetermined arrangement. The allocation of joint profit to each business may not correspond to the percentage of supply or incurred costs. The central administrative body determines the output quota for each business to minimize production costs. This occurs when the marginal costs of the member businesses are equivalent (Pindyck et al, 2009).

To ascertain the price and production of a cartel, we examine a two-member company. The cartel's industrial demand curve is shown as its aggregate demand curve, denoted as DD in the image below. The marginal revenue curve of the cartel is positioned underneath the demand curve. The marginal cost curve of the cartel (MCT) is the horizontal summation of the marginal cost curves of businesses A and B (MCA and MCB). The production of each business is allocated so that the marginal costs are equivalent (Shapiro, 1989). The cartel's profit is optimized at the point when marginal revenue equals marginal cost, shown here as point C. The output that maximizes profit is OQ*, and the corresponding price is OP*. The graphic illustrates that when business A produces OQ1 and firm B produces OQ2, their marginal costs are equivalent. OQ* represents the aggregate of OQ1 and OQ2, together A's profit PFTK and B's PEGH, yielding a maximum total (Hall et al, 2010).

The specified demand function is

P = 1,000 - QS - QT 

QS and QT represent the amounts sold by the different businesses, whereas P denotes the market selling price. The total cost functions for the production and sale of the component for the individual enterprises are:

TCs = 70,000 + 5QS + 0.25Q²S

TCt = 110,000 + 5QT + 0.15Q²T 

The total profit of S is:

P_S = P_Qs - T_Cs = (1000 - Q_s - Q_t)Qs = 70,000 + 5QS + 0.25Q²S

-70000 + 995QS - QsQT - 1.25Qs²

The partial derivative of the aforementioned equation with regard to Qs yields (Varian, 2010):

dPs/dQs = 995 - Qt - 2.50Qs………………………………… (1)

In a similar manner, we calculate company T's total profit as follows:

Π T = P T - T C T = (1000 - Q S - Q T) QT = 110,000 + 5QT + 0.15Q²T

-110000 + 995QT - QS QT - 1.15QT² 

Upon computing the partial derivatives with respect to Qt, we derive the following:

dPt/dQT = 995 - QS - 2.3QT................................................(2)

The first equation represents functions of QS and QT.

Equating both equations 1 and 2 to zero results in:

2.50Q_s + Q_t = 995

Qs + 2.30Qt = 995

Upon solving the two equations, we get QS* = 272.32 units and QT* = 314.21 units. By inserting these two numbers into the demand equation, we get the equilibrium selling price of P* = $413.47 per unit, and the resultant profits are:

Π S = $22,695

Π T = $3536.17.

b) If both enterprises choose to establish a cartel, the total industry earnings would be:

 π = πs + πt

PQS minus TCS plus PQT minus TCT

π = (1000 - Qs - Qt) Qs = 70,000 + 5QS + 0.25Q²S + (1000 - Qs - Qt) Qt = 110,000 + 5QT + 0.15QT²

180000 + 995Qs - 1.25Qs² + 995Qt - 1.15Q² - 2QsQt

To optimize overall profit, we compute the partial derivatives with regard to Qs and Qt, respectively.

dPR/dQs = 995 - 2.50Qs - 2Qt

dPR/dQt = 995 - 2.30Qt - 2Qs

By equating them to zero, we derive:

995 - 2.50Q_s - 2Q_t = 0

995 - 2.30Qt - 2Qs = 0

Upon resolution, we get Qs* = 170.57 units and Qt* = 284.39 units. Substituting these values into the pricing functions and profit function yields P* = $545.14 per unit and PR* = $46,291.43.

The marginal costs for each business are as follows:

MCs = d(TCs)/dQs = 5 + 0.5Qs

MCt = d(TCt)/dQt = 5 + 0.3Qt

Upon replacing values into the previously derived marginal cost function, we obtain: MCs = MCt = $90.29

Reference

Pindyck, R. Rubinfeld, D. & Mehta, P. (2009). Microeconomics. South Asia: Pearson

Hall, R., & Lieberman, M., ( 2010). Economics: Principles and applications, USA: CengagE learning

Shapiro, C. (1989). Theories of Oligopoly behavior. Available at: https://www.sciencedirect.com/science/article/pii/S1573448X89010095 [Accessed 9 March 2017]

Varian, H. (2010). Intermediate microeconomics. New Delhi:Affiliated East-West Press