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(a) Suppose a monopolist sells its product in two different markets separated by some distance. The demand curves in the markets given by q1 = 110 -2p1 and q2 = 35 - pz. Marginal and average costs are constant at Rs. 15. (i) If the monopolist can maintain the separation between the two markets, what are total profits in this situation? (ii) Suppose the firm could adopts a linear two part tariff under which marginal prices must be equal in the two markets but lump-sum entry fee might vary. What pricing policy (third degree price discrimination or linear two part tariff) should the firm follow? b) The payoff matrix of the two rival players is given as; Player 2 L R Player 1 T 4.4 2.6 B 6.2 0.0 (i) Find the pure-strategy Nash equilibrium or equilibria. Compute the mixed-strategy Nash equilibrium. As part of your answer, draw the best- response function diagram for the mixed strategies. (iii) Suppose the game is played sequentially, with player 1 moving first. Write down the normal and extensive forms for the sequential version of the game. (iv) Using the normal form for the sequential version of the game, solve for the Nash equilibria. (v) Identify the proper sub-games in the extensive form got the sequential version of the game. Use backward induction to solve for the subgame-perfect equilibrium. Explain why the other Nash equilibria of the sequential game are "unreasonable'. (c) Explain marginal cost pricing dilemma that arises under natural monopoly. (a) There is a 50 KM long beach which has two ice cream stands, A and B, located at 20 KM and 35 km respectively, from the starting point. They sell identical ice cream cones, which for simplicity are assumed to be costless to produce. The buyers of ice cream cones are located uniformly along the beach, one at each unit of length. Each buyer consumes one cone daily. Carrying ice cream a distance 'd' back to one's beach umbrella costs 0.05d', where d is the distance (in km) of the buyer from the ice cream stand. In the context of Hotelling's Beach location model; (i) Find the location of the buyer who is indifferent between buying ice cream from A and B. (ii) Find the total sales of ice cream one ice cream cone. (iii)Find the equilibrium prices chaName: Student ID: Section: Part 4: What is the value of Real GDP in Belgium in 2016? Part 5: What is the value of Real GDP in Belgium in 2017? Part 6: Calculate the growth rate of Real GDP between 2016 and 2017. Round your answer to the nearest hundredth of one percent. Part 7: You may have noticed that Nominal GDP grew more quickly than Real GDP between 2016 and 2017. Why does this make sense?8 HANDOUT LAB EXERCISE TO FOLLOW LAB EXERCISE $ IN LAB BOOK 3. Fill in the blanks below so that they match the N bases and sugars on your DNA sketch on the previous page. You will be able to fill in the right hand side of the molecule below. To fill in the left hand side, you will need to use the principle of complimentarity. Use the first letter of the words for each base and sugar. The letter "P" represents the phosphate group. The dots represent the bonds between complimentary nucleotides. bonds are holding the complimentary N bases together. bonds are holding the nucleotides together as a polymer. (#) total nucleotides are present in the molecule. (#) total N bases are present in the molecule.(a) Consider this quote: "If an estimator is unbiased, then its probability distribution has an expected value equal to the parameter it is supposed to be estimating" . Explain this quote with reference to the concept of 'repeated sampling'. (4 marks) (b) Draw a diagram illustrating the example of two unbiased estimators that have different levels of efficiency. Which estimator would you prefer to use and why? (2 marks) (c) State the Central Limit Theorem (CLT) using the example of a random variable X which has a uniform distribution. In this particular example, we take successive, independent sub-samples of n=2 from the population represented by random variable X to obtain alternative estimates of the sample mean X . We then study the distribution of these sample means Y n across repeated samples. (4 marks)2. Algebraic manipulation example In this next set of exercises, we are going to prove a useful statement in two ways: first by using the real-valued trigonometric functions, and next by using the complex-exponential representation of the same trigonometric functions. This exercise will serve to show the close relationship between complex exponential functions and trigonometric functions. Following is a true general statement regarding periodic oscillations: A periodic oscillation at angular frequency w can be represented in general by f(t) = A cos(wt + (), where A represents the amplitude and o represents the phase factor. This same periodic oscillation can be represented by f(t) = Bcos(wt) + C sin(wt) for an appropriately chosen constants B and C. In other words, f(t) = A cos(wt + $) = Bcos(wt) + Csin(wt) and we will come up with formulas for B and C in terms of A and @ and prove this statement in the next set of exercises, starting with the first method using real-valued trigonometric functions. a. First method: The strategy here is to expand out the left-hand side (A cos(wt + ) ) using the angle addition formula. Using one of the angle addition formulas, expand out the left-hand side and fill in the blanks below (watch out for signs). A cos(wt + p) = A( cos(wt) + [Format Hint: (1) Use "*","+","-", and "/" for multiplication, addition, subtraction, and division. (2) Spell out Greek letters (e.g. "omega" for w). (3) Use the usual name for functions ("sin", "cos", "tan", etc.).] b. For this equality to hold for all time t, the coefficients to the cos(wt) terms on left- and right- hand sides should be equal to each other, and the coefficients to the sin(wt) terms on left- and right-hand sides should be equal to each other. We call this "collecting like terms" or "comparing like terms" (remember the phrase "like terms" from algebra?). Fill in the blanks below by comparing like terms: B = , and C =
