Question One a) Explain how resources are allocated in a free market system. b) Differentiate between private costs and social costs. 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 quantity. [4 Marks] iii.Plot, on one set of axes, the market demand curve and the market supply curve for commodity X and show the equilibrium point. [4 Marks] [5 Marks] [4 Marks)

a) In a free market system, resources are allocated through the interaction of supply and demand. Producers and consumers make decisions based on their own self-interest, and prices are determined by the market. The price mechanism plays a crucial role in allocating resources efficiently. When there is a shortage of a particular good, its price will rise, signaling producers to increase production and consumers to reduce consumption. Conversely, when there is an excess of a good, its price will fall, indicating producers to reduce production and consumers to increase consumption.<br /><br />b) Private costs refer to the costs incurred by an individual or firm when producing or consuming a good or service. These costs are borne by the producer or consumer directly involved in the transaction. Social costs, on the other hand, include both private costs and any external costs or benefits that affect third parties who are not directly involved in the transaction. For example, the cost of pollution from a factory is a social cost, as it affects the surrounding community, even though it is a private cost for the factory owner.<br /><br />c) To encourage innovations amid fear of externalities, the government can implement various measures. One approach is to provide incentives for innovation, such as tax breaks, subsidies, or grants to researchers and businesses. Additionally, the government can establish intellectual property rights, such as patents and copyrights, to protect innovators and encourage investment in research and development. Another strategy is to internalize externalities through regulations or taxes. For instance, the government can impose a tax on polluters to account for the social cost of pollution or regulate emissions to ensure that producers and consumers take into account the externalities associated with their actions.<br /><br />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 consumer and producer, respectively.<br /><br />Market demand function: $Qd_{x} = 10,000 \times (12 - 2P_{x}) = 120,000 - 20,000P_{x}$<br /><br />Market supply function: $Qs_{x} = 1,000 \times (20P_{x}) = 20,000P_{x}$<br /><br />ii. To find the market demand schedule and market supply schedule of commodity X, we need to substitute different price levels into the market demand and supply functions and calculate the corresponding quantities.<br /><br />Market demand schedule:<br /><br />| Price ($P_{x}$) | Quantity Demanded ($Qd_{x}$) |<br />| --- | --- |<br />| 0 | 120,000 |<br />| 1 | 100,000 |<br />| 2 | 80,000 |<br />|... |... |<br /><br />Market supply schedule:<br /><br />| Price ($P_{x}$) | Quantity Supplied ($Qs_{x}$) |<br />| --- | --- |<br />| 0 | 0 |<br />| 1 | 20,000 |<br />| 2 | 40,000 |<br />|... |... |<br /><br />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.<br /><br />$120,000 - 20,000P_{x} = 20,000P_{x}$<br /><br />$120,000 = 40,000P_{x}$<br /><br />$P_{x} = 3$<br /><br />Substituting the equilibrium price back into either the demand or supply function, we can find the equilibrium quantity.<br /><br />$Qd_{x} = 120,000 - 20,000 \times 3 = 90,000$<br /><br />$Qs_{x} = 20,000 \times 3 = 60,000$<br /><br />iii. To plot the market demand curve and the market supply curve for commodity X, we can use the market demand schedule and market supply schedule. The equilibrium point is where the demand curve intersects the supply curve, which is at the equilibrium price and equilibrium quantity.<br /><br />[Note: As an AI language model, I cannot physically plot the graphs. However, you can use graphing software or graph paper to plot the curves and show the equilibrium point.]