1. (a) Define price control.

(b) With the aid of a well labelled diagram, explain the two types of price controls

1. (a) Define price control.

Price control refers to government-mandated minimum or maximum prices for goods and services. These controls are implemented to address market failures, such as price gouging during shortages or to protect consumers from excessively high prices. They can take the form of price ceilings (maximum prices) or price floors (minimum prices).

(b) With the aid of a well labelled diagram, explain the two types of price controls

The two main types of price controls are price ceilings and price floors. Let's examine them with the help of a supply and demand diagram.

(Note: Since I cannot create images directly, please imagine a standard supply and demand graph. The vertical axis represents price (P), and the horizontal axis represents quantity (Q). The supply curve (S) slopes upward, and the demand curve (D) slopes downward. The equilibrium price (Pe) and quantity (Qe) are where the two curves intersect.)

Price Ceiling: A price ceiling is a maximum legal price that can be charged for a good or service. On the diagram, it's represented by a horizontal line below the equilibrium price (Pe). The effect is that the quantity demanded (Qd) exceeds the quantity supplied (Qs), leading to a shortage. The shortage size is the difference between Qd and Qs at the controlled price.

Examples of Price Ceilings: Rent control in some cities, price caps on essential goods during emergencies.

Price Floor: A price floor is a minimum legal price that can be charged for a good or service. On the diagram, it's represented by a horizontal line above the equilibrium price (Pe). The effect is that the quantity supplied (Qs) exceeds the quantity demanded (Qd), resulting in a surplus. The surplus size is the difference between Qs and Qd at the controlled price.

Examples of Price Floors: Minimum wage laws, agricultural price supports.

Consequences of Price Controls: Both price ceilings and floors can have unintended consequences. Price ceilings can lead to shortages, black markets, and reduced quality. Price floors can lead to surpluses, inefficiency, and wasted resources. The effectiveness of price controls depends on factors such as the elasticity of supply and demand, the ability of producers and consumers to adjust their behavior, and the enforcement mechanisms in place.

1.

a) List the four known forces in physics.

1. List the four known forces in physics;
2. Which of these forces is responsible for holding the nucleons together in a nucleus;
3. Give two characteristics of this force;

b) i. Give four characteristics of identifying elementary particles;

ii. What are the three groups, into which elementary particles can be divided, indicating which force is responsible for each group and the corresponding statistics of the group?

c) Using the Nuclear Matter expression for the nuclear radius, R, with mass number, A; and charge Ze uniformly distributed in the nucleus, show that:

1. its Coulomb energy is
2. the energy of the emitted positron when ¹³N₇ decays to its mirror nucleus ¹³Al₁₃ is between the mirror nuclei. r₀ = 1.3 fm.

Hint: use Gauss' law to determine the electric field created by a uniformly charged sphere

1. Answer

a)

1. The four known forces in physics are:
   • Strong Nuclear Force: Responsible for binding protons and neutrons together in the nucleus.
   • Electromagnetic Force: Governs interactions between electrically charged particles.
   • Weak Nuclear Force: Responsible for radioactive decay processes like beta decay.
   • Gravitational Force: The force of attraction between any two objects with mass.
2. The strong nuclear force is responsible for holding nucleons together in a nucleus.
3. Two characteristics of the strong nuclear force are:
   • Short Range: Its influence is significant only over very short distances (approximately the size of a nucleus).
   • Charge Independent: It acts equally between proton-proton, proton-neutron, and neutron-neutron pairs.

b)

1. Four characteristics of identifying elementary particles:
   • Mass: Each elementary particle has a specific rest mass.
   • Charge: Particles can be electrically charged (positive, negative, or neutral).
   • Spin: An intrinsic angular momentum quantum number.
   • Lifetime: Some particles are stable while others decay into other particles.
2. The three groups of elementary particles are:
   • Quarks: Fundamental constituents of hadrons (protons, neutrons, etc.). The strong force governs their interactions, and they obey Fermi-Dirac statistics.
   • Leptons: Fundamental particles that do not participate in the strong interaction. Examples include electrons and neutrinos. The weak and electromagnetic forces govern their interactions; they obey Fermi-Dirac statistics.
   • Gauge Bosons: Force-carrying particles that mediate fundamental interactions. Examples include photons (electromagnetism), gluons (strong force), and W and Z bosons (weak force). They are bosons and obey Bose-Einstein statistics.

c)

1. Coulomb Energy: To find the Coulomb energy, consider a uniformly charged sphere with radius R and total charge Ze. Using Gauss's law, the electric field at a distance r (r ≤ R) from the center is given by:
   E(r) = (1/(4πε₀)) * (Ze * r/R³)
   The potential energy dU of a shell of charge dq at radius r is:
   dU = V(r)dq = (1/(4πε₀)) * (Ze * r/R³) * (4πr²) * (Ze/A)(dr/R)
   Integrating from 0 to R to obtain the total Coulomb energy:
   
2. Energy of the emitted positron: The energy difference between the mirror nuclei (¹³N₇ and ¹³Al₁₃) is primarily due to the Coulomb energy difference. The mass difference is converted into energy in the form of a positron. The calculation requires considering the mass difference between the isotopes and using Einstein's mass-energy equivalence (E=mc²). The provided formula needs further derivation to incorporate the mass difference and the effect of nuclear binding energy.

2. Mention and explain the phases of colonial movement in Africa.

The colonial movement in Africa unfolded in distinct phases, though the exact periodization can be debated depending on the specific region and historical interpretations. A common framework identifies the following phases:

1. Early Exploration and Penetration (Late 15th - Mid 19th Century): This initial stage involved primarily European exploration, driven by trade interests (e.g., the slave trade). Contact was limited, focused on coastal areas and specific commodities. It laid the groundwork for later colonization but didn't constitute widespread direct rule. Examples include the Portuguese presence along the African coast and initial British and French trading posts.
2. The Scramble for Africa (1880s-1914): This period witnessed a rapid surge in European colonization. Fueled by industrialization, nationalism, and the perceived need for raw materials and markets, European powers rapidly partitioned the African continent through treaties, military force, and diplomatic maneuvering. The Berlin Conference (1884-1885) is a key event symbolizing this scramble, where European powers established rules for claiming African territories without much regard for pre-existing African political structures or boundaries.
3. Direct Rule and Colonial Administration (Early 20th Century): Following the scramble, European powers established direct administrative control over their colonies. This involved setting up bureaucratic structures, establishing military presence, and implementing various policies designed to extract resources and suppress resistance. Administrative strategies varied, with some employing indirect rule (using existing local leaders), while others opted for more direct forms of governance.
4. Resistance and Nationalist Movements (Early to Mid 20th Century): Colonial rule wasn't met with passive acceptance. African resistance movements, both armed and non-violent, sprang up throughout the continent, challenging colonial authority. The rise of nationalist ideologies and movements during the mid-20th century gained momentum, fueled by World War II, the rise of pan-Africanism, and the growing global support for decolonization.
5. Decolonization and Independence (Mid 20th Century - Onward): The post-World War II era witnessed the dismantling of colonial empires. Many African nations achieved independence, although the legacy of colonialism continues to shape African societies economically, politically, and socially. The process of decolonization wasn't always peaceful and often involved negotiation, armed struggle, and transitions marked by internal political instability.

It is crucial to understand that these phases weren't neatly separated and often overlapped. Furthermore, the experience of colonization varied significantly across different parts of Africa, shaped by specific historical circumstances, the nature of colonial administration, and the resistance encountered by European powers.

1. Pricing decision is very central to product planning and profitability of corporate organisations. You are required:

1. (a) Outlines four factors to be considered in pricing decision

2. (b) Distinguish cost-based from competitor - based pricing

3. (c) Describe three objectives of a transfer pricing system

4. (d) ALHIKMAH Nigeria limited manufactures one product. It has recently commissioned a marketing research firm to estimate the quantity of the product likely to be demanded annually at different selling prices. The results are as follows:

   Price (N):	20	40	60	80	100
   Demand (units):	24,000	20,000	16,000	12,000	8,000

   The company is currently, charging a price of 440 and is selling 20,000 units annually. Variable cost amount to N20 per unit produced and sold. The company incurs fixed cost of 40,000 per annum. You are required to determine the optimal selling price of the company's product

1. Pricing Decision

1. (a) Four Factors to Consider in Pricing Decisions:

   • Cost of Production: This includes direct materials, direct labor, manufacturing overhead, and other relevant costs. Accurate cost accounting is crucial for setting a price that covers costs and provides a profit margin.
   • Market Demand: Understanding the demand elasticity (how sensitive demand is to price changes) is vital. High demand might allow for higher prices, while low demand necessitates lower prices to remain competitive. Market research is essential for this assessment.
   • Competition: Analyzing competitor pricing strategies and product offerings is necessary. Prices must be competitive enough to attract customers but also profitable. This involves studying competitor costs, market positioning, and pricing strategies.
   • Company Objectives: Pricing strategies should align with overall business goals (e.g., maximizing profit, increasing market share, building brand image). Short-term profit maximization might differ from long-term market share goals. The selected pricing strategy reflects these overarching objectives.

2. (b) Cost-Based vs. Competitor-Based Pricing:

   • Cost-Based Pricing: This method sets prices based on the cost of production, plus a markup for profit. The formula is typically: Price = Cost + (Cost × Markup Percentage). It's simple but may not consider market realities or competitor actions.
   • Competitor-Based Pricing: This strategy sets prices based on what competitors are charging for similar products. It focuses on market competitiveness, but might ignore individual cost structures and profitability.

3. (c) Three Objectives of a Transfer Pricing System:

   • Profit Maximization for the Overall Organization: The system should ensure that pricing between divisions leads to the highest overall profit for the entire company, not just individual units.
   • Fairness and Equity Between Divisions: Transfer prices should be perceived as fair by all divisions, encouraging cooperation and preventing conflict. A perceived unfair transfer price can demotivate divisions.
   • Compliance with Tax Regulations: Transfer pricing must comply with tax laws in different jurisdictions to avoid penalties and legal issues. Tax authorities scrutinize transfer pricing to ensure that companies are not artificially shifting profits to low-tax regions.

4. (d) Optimal Selling Price for ALHIKMAH Nigeria Limited:

   To find the optimal selling price, we need to calculate the total revenue, total cost, and profit for each price point. Then, we find the price that yields the highest profit.

   Price (N)	Demand (units)	Total Revenue (N)	Variable Cost (N)	Fixed Cost (N)	Total Cost (N)	Profit (N)
   20	24000	480000	480000	40000	520000	-40000
   40	20000	800000	400000	40000	440000	360000
   60	16000	960000	320000	40000	360000	600000
   80	12000	960000	240000	40000	280000	680000
   100	8000	800000	160000	40000	200000	600000

   Based on this analysis, the optimal selling price is N80, as it yields the highest profit of N680,000.