RRefer to the... questions below.
10.2. Exercises (1) Suppose that the derivative of a function f is given by /'() = = r+3, I+2 I-4' . Then the intervals on which f is increasing are ( ) and ( (2) Suppose that the derivative of a function f is given by S'(r) = -T (r+ 1) (a) The interval on which the function f is increasing is ( (b) Estimate to two decimal places the location of a point r > 0 where f has a point of inflection. Answer: _ (3) A function f is defined on the interval [0, x]. Its derivative is given by f'(r) = cos r-sin 2r. (a) The intervals on which f is increasing are (a, - ) and (= , ") where a = b= _, C=_ -, and d = _ (b) Estimate to two decimal places the location of points of inflection. Answer: 1, _ and 2. (4) Suppose that the derivative of a function f is given by f'(x) = (x - 2)3(x + 4). (a) The interval on which f is increasing is ( . (b) f has no local (c) f has a local at r = (5) Suppose that the derivative of a function f is given by f'(r) = - r+1 VI +1 (a) The interval on which f is increasing is ( (b) f has no local (c) f has a local at r= (6) Suppose that the derivative of a function f is given by f'(r) = In(1 + 12). (a) The interval on which f is increasing is ( . ). (b) At how many points does f have a local maximum? Answer: (c) At how many points does f have a local minimum? Answer: (d) The interval on which f is concave up is ( ) . (e) f has a point of inflection at r = (7) Suppose that the derivative of a function f is given by S'(r) = (a) The interval on which f is increasing is ( _ (b) At how many points does f have a local maximum? Answer: (c) At how many points does f have a local minimum? Answer: (d) The interval on which f is concave up is (. (e) f has a point of inflection at r = (8) Suppose that the derivative of a function f is given by S'(r) = (a) The interval on which f is increasing is (_ (b) At how many points does f have a local maximum? Answer: (c) At how many points does f have a local minimum? Answer: (d) The interval on which f is concave up is ( (e) f has points of inflection at 1 = and : = 10.2. EXERCISES 61 (9) The domain of a function f is [a. o). Below is a sketch of the graph of the derivative of f. (a) The largest intervals on which / is increasing are ( _) and (b) / has local minima at r = _ _ and r = (c) The largest intervals on which f is concave up are (_ _) and (_ (d) f has points of inflection at: r =_ and r = (10) The domain of a function f is [o, el. Below is a sketch of the graph of the derivative of f. (a) The largest interval on which / is increasing is (_ - -97. The Reserve Bank of India calculates four components of money supply, Me, My, M and My. Select the incorrect pair out of the following: (a) Mi = includes currency and coins with the public; demand deposits of the banks and other deposits with the RBI (b) My = includes M, and demand deposits of the post offices (c) M, = includes the sum of M, and My (d) M. = includes the sum of My and demand as well as time deposits of post officesb) As explained in lecture and in the text, the balanced budget multiplier equals 1. Explain how your answers to (2a) and (3a) confirm that the balanced budget multiplier is indeed31. Consumers distributed uniformly along a straight-line road are the potential market for two duopoloists whose decision problem is where to locate their sales offices. Demand is completely inelastic, and consumers will purchase from whichever sales office is nearer. Assume that the road is 4 miles long and that, for simplicity, each firm has exactly five possible strategies: it may locate itself at either end or at the 1-mile, 2-mile, or 3-mile markets. Let the payoffs to the duopolists be their respective market shares. (a) Is this a zero-sum (or constant-sum) game? (b) What is the payoff matrix? (c) What are optimal strategies for the duopolists?48. Consider the following statements and select the correct code given below : 1. Gallup Poll is immensely used for market research and election forecasting, named after the US statistician who developed it. 2. Galloping inflation is a kind of hyperinflation, which behaves the way Gallup survey is conducted. CODE : (a) Only 1 (b) Only 2 (c) Both 1 and 2 (d) Neither I nor 213. A consumer who obeys the von Neumann-Morgenstern axioms and has an initial wealth of 160,000 is subject to a fire risk. There is a 5 percent probability of a major fire with a loss of 70,000 and a 5 percent probability of a disastrous fire with a loss of 120,000. Her utility function is U = WO-. She is offered an insurance policy with the deductibility provision that she bear the first 7620 of any fire loss. What is the maximum premium that she is willing to pay for this policy?36. Consider an economy with two consumers, two public goods, one ordinary good, one implicit production function, and a fixed supply of one primary factor that does not enter the consumer's utility functions. Determine the first-order conditions for a Pareto-optimal allocation. In particular, what combination of RCSs must equal the RPT for the two public goods?Problem 6. Logistic population growth: suppose the growth rate of a population of wild fish is given by F(x) = 10x - 0.01x- if the population is left undisturbed, were x is population. a What is the equilibrium natural population? b. What is the maximum sustained yield, and the corresponding population? c. Graph the population growth function. Which portions of this function correspond to biological overfishing?24. Consider the following markets which are characterized by lagged supply response: (a) D, = 40 - 10p ; S, = 2 + 9p.1. (b) D. =30-5p ; St = 20- pul. Determine equilibrium price and quantity for each market. Assume an initial price 20 percent below the equilibrium price for each market, and determine the number of periods necessary for each price to adjust to within 1 percent of equilibrium
