DURATION Instructions: Answer ALL Question Question One 1. Differentiate between risk-neutral and risk loving preferences. (2marks) II. Illustrate how the shape of an individual's utility function describes his or her attitudes toward (3Marks) risk III. Suppose that you have a utility function given by the equation \( U=\sqrt{501} \). Consider a lottery that provides a payoff of OFCFA with probability 0.75 and \( 20,000 \mathrm{FCFA} \) with probability 0.25 . a. Sketch a graph of this utility function, letting I vary over they range 0 to 200. (5marks) b. Verify that the expected value of this lottery is 5000 FCFA (5marks) With the use of diagrams, differentiate between profit making and profit maximization (3 Marks) Question Two (3 Marks) , Answer true or false: b. The supply curve in a Monopoly is the section of the MC curve that lies above the AC curve c. The demand curve in a perfect competitive market is downward sloping. (1 Mark) d. Given a demand function of two firms operating in a Cournot Oligopoly Market. \[ Q=200-P: \] Were \( Q= \) Quantity demanded and \( P= \) price Determined the reaction function of each firm operating in this market Illustrate the Cournot equilibrium on a graph. What quantity should each firm produce? What profit will each firm be making? (3 Marks) (3 Marks) (2 Marks) (2 Marks)

When it comes to risk-neutral and risk-loving preferences, risk-neutral individuals view uncertain outcomes purely by their expected values, showing indifference between risky and certain options. In contrast, risk-loving individuals prefer options with higher levels of uncertainty, deriving utility from the thrill of potential high gains, even if these come with increased risks. This means they tend to choose lotteries or investments that have a chance of significant outcomes rather than opting for more guaranteed returns. The shape of an individual's utility function can reveal a lot about their risk attitudes. A concave utility function indicates risk aversion, as the individual derives diminishing returns from increasing wealth. This means they prefer a certain outcome over a risky one with the same expected value. Conversely, a convex utility function characterizes risk-seeking behavior, as individuals display increasing marginal utility from wealth, showing they are more likely to take risks for the chance of higher payoffs. For verifying the expected value of the lottery with payoffs of OFCFA with probability 0.75 and 20,000 FCFA with probability 0.25, you'd compute it as follows: \(EV = (0.75 \times OFCFA) + (0.25 \times 20,000)\). Since we need to find an expected value of 5,000 FCFA, set the equation up properly: \(0.75 \times OFCFA + 5,000 = 5,000\) will give you the necessary calculations to solve for OFCFA. Illustrating profit-making versus profit maximization can be illustrated through a standard graph: the profit-making area would encompass any region where total revenue exceeds total cost, while profit maximization specifically finds the output level where marginal cost equals marginal revenue—this would be a single point on the graph showcasing maximum efficiency and output. For the true or false statements, b is true because the supply curve for a monopoly refers to the segment of the marginal cost curve that is above the average cost curve. c is false; in a perfectly competitive market, the demand curve faced by an individual firm is perfectly elastic (horizontal), not downward sloping. To find the reaction functions for each firm in the Cournot oligopoly model, use the given demand function \(Q = 200 - P\). Each firm will set its output based on the other's output, leading to reaction functions \(q_1 = (200 - q_2)/2\) and \(q_2 = (200 - q_1)/2\). Graphing these can help visualize how each firm's production quantity interacts. Both firms optimally produce at Cournot equilibrium, where the total quantity is divided between them according to their reaction functions, and profits can be calculated using the market price derived from substituting their combined output back into the demand function.