Question one (Compolisary) the fillswing fundamental concepts. (i) Scarcity and Cheice (4 marks) (10) Opportanity cost ( ) marks) (iii)Production possibility fruetier (1) marks) (4 marks) b) The following economic functions have been derived by the Finance Manager of the Kenya Tea Limited: Q_(A)=3P^2-4PandQ_(B)=24-P^2 where prepresents price and Q is quantity Required: (i) Which of the two functions represents a demand curve, supply curve and why? (3 marks) (ii) At what values of price and quantity Is the market in equilibrium? (4 marks) (iii)Explain, with the aid of a diagram, the effict on the demand and supply functions indicated in (a) above of a simultaneous decrease in cost of proficien and an increase in the price of a complementary good. (4 marks) Question Two a) Discuss what you understand with consumer sourceipty and indicate in limits b) (i) Defleas in ledifference curve (6 marks) (2 marks) (ii) Illustrate and claudy explain the reture of indifference carves for perfect substitution and for complementary good (4 marks) (iii) Explain the property of convexity to the origin of an indifference canse ( ) marks) Question Three a) State the law of variable proportions and highlight to hay ansumptions (7 marks) b) Using an illustration discuss the main stages of production amociated with the law of variable proportion. Which stage will you recommend for production __ (it marks)

Question One:<br />a) The correct answer is (i) Scarcity and Choice (4 marks), (ii) Opportunity cost (4 marks), (iii) Production possibility frontier (1 mark), and Normative economics (4 marks).<br /><br />b) <br />(i) The function Q_A = 3P^2 - 4P represents a supply curve because it shows the quantity supplied (Q_A) as a function of price (P). The function Q_B = 24 - P^2 represents a demand curve because it shows the quantity demanded (Q_B) as a function of price (P). This is because, in general, the supply curve is upward sloping, indicating that as the price increases, the quantity supplied also increases. On the other hand, the demand curve is downward sloping, indicating that as the price increases, the quantity demanded decreases.<br /><br />(ii) To find the market equilibrium, we need to set the quantity supplied equal to the quantity demanded and solve for the price and quantity. Equating Q_A and Q_B, we get 3P^2 - 4P = 24 - P^2. Solving this equation, we find P = 4 and Q_A = Q_B = 8. Therefore, the market is in equilibrium at a price of 4 and a quantity of 8.<br /><br />(iii) A simultaneous decrease in the cost of production and an increase in the price of a complementary good will shift the supply curve to the right and the demand curve to the right, respectively. This is because a decrease in the cost of production will increase the quantity supplied at each price level, shifting the supply curve to the right. On the other hand, an increase in the price of a complementary good will increase the quantity demanded at each price level, shifting the demand curve to the right. The resulting equilibrium price and quantity will depend on the magnitude of the shifts in the supply and demand curves.<br /><br />Question Two:<br />a) Consumer sovereignty refers to the idea that consumers are the ultimate decision-makers in the economy. They determine what goods and services are produced by their purchasing decisions. In other words, consumers have the power to decide what is produced by choosing what to buy. The limits of consumer sovereignty include factors such as income constraints, preferences, and the availability of information.<br /><br />b) <br />(i) An indifference curve is a graphical representation of a consumer's preferences. It shows the different combinations of two goods that provide the same level of satisfaction or utility to the consumer.<br /><br />(ii) Indifference curves for perfect substitution and complementary goods can be illustrated as follows:<br /><br />For perfect substitution, the indifference curve is a straight line, indicating that the consumer is indifferent between the two goods. For example, if good X and good Y are perfect substitutes, the consumer is equally satisfied with any combination of X and Y that provides the same total utility.<br /><br />For complementary goods, the indifference curve is convex to the origin, indicating that the consumer prefers a specific combination of the two goods. For example, if good X and good Y are complements, the consumer is less satisfied with any combination of X and Y that deviates from the optimal combination.<br /><br />(iii) The property of convexity to the origin of an indifference curve indicates that the consumer prefers a balanced combination of the two goods. It suggests that the consumer is willing to give up some amount of one good to obtain more of the other good, but not at a constant rate. The convex shape of the indifference curve reflects the diminishing marginal rate of substitution, which means that the consumer is willing to give up less and less of one good to obtain additional units of the other good.<br /><br />Question Three:<br />a) The law of variable proportions states that as more units of a variable input (such as labor) are added to fixed inputs (such as capital), the marginal product of the variable input will eventually decrease. The key assumptions of the law of variable proportions include the presence of at least one fixed input, the presence of a variable input, and the assumption that the technology or production process remains constant.<br /><br />b) The main stages of production associated with the law of variable proportions can be illustrated as follows:<br /><br />1. Increasing returns stage: In this stage, the addition of more units of the variable input leads to an increasing marginal product. This is because the fixed inputs are being utilized more efficiently.<br /><br />2. Diminishing returns stage: In this stage, the addition of more units of the variable input leads to a decreasing marginal product. This is because the fixed inputs become overutilized, and the additional units of the variable input contribute less and less to the overall output.<br /><br />3. Negative returns stage: In this stage, the addition of more units of the variable input leads to a negative marginal product. This is because the fixed inputs are being overutilized to the point where adding more units of the variable input actually reduces the overall output.<br /><br />Based on the law of variable proportions, I would recommend the diminishing returns stage for production. This stage is characterized by a decreasing marginal product, which means that the addition of more units of the variable input