QUESTION FIVE a) The market for sugar is represented by the following models: Q_(d)=90-0.5P and Q_(s)=-30+1.0P i. Find the levels of output and price at which the market is at equilibrium (4 marks) ii. What would happen to the market when government fixes price at the following levels: P=36,P=30,P=48 (4marks) 111 What would be the new market condition if Price elasticity of demand changed to 0.75 (4 marks) iV What would happen to the market if price elasticity of supply is unitary (4 marks) Identify and Explain the three distinct Economics systems (4 marks)

i. To find the levels of output and price at which the market is at equilibrium, we need to set the quantity demanded equal to the quantity supplied and solve for the price and quantity.<br /><br />$Q_{d} = Q_{s}$<br />$90 - 0.5P = -30 + 1.0P$<br />$120 = 1.5P$<br />$P = 80$<br /><br />Substituting the price back into either the demand or supply equation, we can find the quantity:<br /><br />$Q_{d} = 90 - 0.5(80) = 10$<br />$Q_{s} = -30 + 1.0(80) = 50$<br /><br />Therefore, the market is at equilibrium when the price is $80 and the quantity is 10.<br /><br />ii. When the government fixes the price at $P=36$, the quantity demanded will be greater than the quantity supplied, resulting in a shortage in the market. When the price is fixed at $P=30$, the quantity demanded will be equal to the quantity supplied, resulting in a market equilibrium. When the price is fixed at $P=48$, the quantity supplied will be greater than the quantity demanded, resulting in a surplus in the market.<br /><br />iii. If the price elasticity of demand changes to 0.75, the demand curve will become flatter, indicating that consumers are less responsive to changes in price. This would result in a higher equilibrium price and a lower equilibrium quantity compared to the original scenario.<br /><br />iv. If the price elasticity of supply is unitary, the supply curve will be perfectly elastic, indicating that producers are perfectly responsive to changes in price. This would result in a horizontal supply curve, where the quantity supplied remains constant regardless of the price level.<br /><br />v. The three distinct economic systems are:<br /><br />1. Market Economy: In a market economy, economic decisions are made by individuals and firms based on supply and demand. The government plays a limited role in economic activities, and the market forces of supply and demand determine the allocation of resources.<br /><br />2. Command Economy: In a command economy, the government plays a central role in economic decision-making. The government determines what goods and services to produce, how to produce them, and who will receive them. The allocation of resources is determined by the government's plans and directives.<br /><br />3. Mixed Economy: A mixed economy combines elements of both market and command economies. In a mixed economy, the government and private sector both play a role in economic decision-making. The government may regulate certain industries, provide public goods and services, and intervene in the market to achieve social and economic objectives. However, the majority of economic decisions are made by individuals and firms based on supply and demand.