Task: Assignment 1 Question One a) Explain how resources are allocated in a free market system. [5 Marks] b) Differentiate between private costs and social costs. [4 Marks) c) Explain measures that can be adopted by the government to encourage innovations amid fear of externalities. [6 Marks] d) There are 10 ,000 identical individuals in the market for commodity X, each with a demand function given by Qd_(x)=12-2P_(x) , and 1000 identical producers of commodity X,each with a function given by Qs_(x)=20P_(x) i.Find the market demand function and the market supply function for commodity X. [2 Marks] ii.Find the market demand schedule and market supply schedule of commodity X and from them find the equilibrium price and equilibrium

a) In a free market system, resources are allocated through the interaction of supply and demand. Producers offer goods and services for sale, while consumers express their preferences through their purchasing decisions. The price mechanism plays a crucial role in this process. When demand for a particular good or service increases, its price tends to rise, signaling producers to increase production. Conversely, when demand decreases, prices fall, prompting producers to reduce production. This interaction between supply and demand ensures that resources are allocated efficiently, as goods and services are produced and consumed based on consumer preferences and market conditions.b) Private costs refer to the costs incurred by individuals or firms directly involved in an economic transaction. These costs are borne by the parties involved in the production or consumption of a good or service. On the other hand, social costs include both private costs and any external costs imposed on third parties. External costs, also known as negative externalities, are costs that affect individuals who are not directly involved in the economic transaction. For example, pollution generated by a factory may affect the health of nearby residents, representing an external cost.c) To encourage innovations amid fear of externalities, the government can adopt several measures. Firstly, the government can provide incentives for innovation, such as tax breaks, subsidies, or grants to researchers and businesses. These incentives can help reduce the financial burden of innovation and encourage investment in research and development. Secondly, the government can establish intellectual property rights, such as patents and copyrights, to protect innovators and ensure they can benefit from their inventions. Additionally, the government can invest in public research and development initiatives to foster innovation and address externalities. By implementing these measures, the government can create an environment that encourages innovation while mitigating the negative effects of externalities.d) i. To find the market demand function and the market supply function for commodity X, we need to sum up the individual demand and supply functions for each participant in the market.Market demand function: Market supply function: ii. To find the market demand schedule and market supply schedule of commodity X, we need to calculate the quantity demanded and quantity supplied at different price levels.Market demand schedule:| Price ( ) | Quantity Demanded ( ) ||----------------|---------------------------|| 0 | 120,000 || 1 | 100,000 || 2 | 80,000 ||... |... |Market supply schedule:| Price ( ) | Quantity Supplied ( ) ||----------------|-------------------------------|| 0 | 0 || 1 | 20,000 || 2 | 40,000 ||... |... |To find the equilibrium price and equilibrium quantity, we need to set the market demand function equal to the market supply function and solve for the price and quantity. Substituting the equilibrium price into either the demand or supply function, we can find the equilibrium quantity. Therefore, the equilibrium price is $3, and the equilibrium quantity is 60,000 units of commodity X.