Questions and Answers of Business Economics And Finance

Show what happens to the equilibrium conditions in Problem 4.23 if autonomous investment drops to 97.If I0 = 97, the IS equation becomes:A fall in autonomous investment, ceteris paribus, leads to a
Find (a) the equilibrium income level and interest rate, and (b) the levels of C, I, Mt, and Mw, when Ms = 275, and(a) For IS:For LM: C = 89+0.6Y = I 120 150i - M = 0.1Y My = 240 250i -
If the money supply in Problem 4.21 increases by 17, (a) what happens to the equilibrium level of income and rate of interest? (b) What are C, I, Mt, and Mw at the new equilibrium?(a) If the money
Find (a) the level of income and the rate of interest that concurrently bring equilibrium to the economy and (b) estimate the level of consumption C, investment I, the transaction-precautionary
If the foreign sector is added to the model and there is a positive marginal propensity to import z, find (a) the reduced form, (b) the equilibrium level of income, and (c) the effect on the
Find (a) the reduced form, (b) the numerical value of Ye, and (c) the effect on the multiplier if an income tax T with a proportional component t is incorporated into the model, givenwhere C0 = 85,
Find (a) the reduced form, (b) the numerical value of Ye, and (c) the effect on the multiplier when a lump-sum tax is added to the model and consumption becomes a function of disposable income (Yd),
Find (a) the reduced form, (b) the value of the equilibrium level of income Ye, and (c) the effect on the multiplier, given the following model in which investment is not autonomous but a function of
Find the equilibrium level of income (Ye), givenwhen C = 125 + 0.8Y, I = 45, and G = 90.From Problem 4.15, we know that the reduced form equation isand when b = MPC = 0.8, the multiplier 1/(1 –b) =
I0 = 75, and G0 = 30. (a) From Section 4.6, Y = C+I+G Substituting the given values and solving for Y in terms of the parameters (b) and exogenous variables (Co, lo, and Go), (b) (1) Y=C+I+G
(a) Find the reduced-form equation and (b) solve for the equilibrium level of income (1) directly and(2) with the reduced-form equation, givenwhere C0 = 135, b = Y = C +I+G C = C + bY 1 = 10 G = Go
Supply-and-demand analysis can also involve more than two interrelated markets. Use the elimination method to find Pe and Qe for each of the three markets, given the system of equations:For
Use the elimination method to find Pe and Qe, givenMultiplying (4.41) by 3,Subtracting (4.43) from (4.42), be careful to change the sign of every term in (4.43) before adding:Using the quadratic
The elimination and substitution methods can also be used to solve systems of quadratic equations.Solve the following system of quadratic supply and demand equations, using the substitution
Given the following system of equations for two complementary goods, trousers t and jackets j, find the equilibrium price and quantity, using the elimination method.Setting Qs = Qd for the
Given the following system of simultaneous equations for two substitute goods, beef b and pork p, find the equilibrium price and quantity for each market, using the substitution method. Q = 15Pb-5
Solve the following systems of simultaneous equations, using the substitution method. (a) (b) Solving (4.27) for y, 12x-7y = 106 8x + y = 82 y = 82-8.x Substituting the value of y from (4.28) into
Solve the following systems of simultaneous equations, using the elimination method. (a) 3x+4y=37 (4.18) 8x+5y=76 (4.19) Multiplying (4.18) by 8 and (4.19) by 3 in preparation to eliminate x, 24x +
Find the break-even point for the firms with the following quadratic total revenue R(x) functions by(1) finding the profit π(x) function, setting it equal to zero, and solving for the x’s; (2)
Find the break-even point for the firms with the following linear total revenue R(x) and total cost C(x) functions by (1) finding the profit π(x) function, setting it equal to zero, and solving for
Find the equilibrium price and quantity for the following mathematical models of supply and demand, using (1) equations and (2) graphs.(2) See Fig. 4-16. Note that Q is placed on the y axis.(2) See
Find the equilibrium price Pe and quantity Qe for each of the following markets using (1) equations and (2) graphs:Substituting Qe = 800 in the supply (or demand) equation,(2) See Fig. 4-15. (a)
Solve each of the following systems of equations graphically by (1) finding the slope-intercept forms and (2) graphing:As seen by the intersection in Fig. 4-6, the solution is x = 2, y = −1.As seen
Give the dimensions of each of the following systems of equations and indicate whether the systemis exactly constrained, underconstrained, or overconstrained.(a) With three equations (n) and four
Indicate the general shape of the following rational functions by finding (1) the vertical asymptote VA, (2) the horizontal asymptote HA, and (3) a small number of representative points on the graph:
The frog population F measured in hundreds in a given region depends on the insect population m in thousands:The insect population in turn varies with the amount of rainfall r given in inches: m(r) =
Environmentalists have estimated that the average level of carbon monoxide in the air is L(n) = (1 +0.6n) parts per million (ppm) when the number of people is n thousand. Assuming that the population
A factory’s cost C(q) is a function of the number of units produced; its level of output q(t) is a function of time. Express the factory’s cost as a function of the time given each of the
Draw a similar set of graphs for a car worth $12,000 with a lifespan of 8 years, given (a) V(t) =187.5t2 – 3000t + 12,000 under accelerated depreciation and (b) V(t) = 12,000 – 1500t under linear
Items such as automobiles are subject to accelerated depreciation whereby they lose more of their value faster than they do under linear depreciation. Assume a car worth $10,000 with a lifetime of 10
The cost of scrubbers to clean carbon monoxide from the exhaust of a blast furnace is estimated by the rational functionwhere C is the cost in thousands of dollars of removing x percent of the carbon
The long-run average cost AC(x) can be approximated by a quadratic function. Find the minimum long-run average cost (LRAC) by finding the vertex of AC(x) and sketch the graph, given(1) Here, with a
Given the following total revenue R(x) and total cost C(x) functions, (1) express profit π as a function of x, (2) determine the maximum level of profit by finding the vertex of π(x), and (3) find
Find the total revenue R functions for producers facing the following linear demand functions:(a) By definition total revenue is equal to price x quantity, orNotice how a total revenue function
Do a rough sketch of the graphs of the following rational functions by finding (1) the vertical asymptote, (2) the horizontal asymptote, and (3) selecting a number of representative points and
Use the three steps outlined in Section 3.6 for graphing y = ax2 + bx +c, to sketch the following quadratic functions:(a) y = −x2 + 10x – 16(b) y = x2 – 8x + 18 (1) With a = 1 > 0, the
Solve the following quadratic equations using the quadratic formula:To see how the same solutions for (a) through (d) can also be obtained by factoring, see Problem 1.11 (c) to (f). For practice with
Solve the following quadratic equations by factoring. (a) x+10x +21=0 From Problem 1.6 (a), x+10x+21= (x+3)(x+7)=0
Determine a number of representative points on the graphs of the following rational functions and draw a sketch of the graph. (a) y = 8 x-4
Graph the following quadratic functions and identify the vertex and axis of each:(a) f(x) = x2 – 2 First select some representative values of x and solve for f(x). Then, using y for f(x), plot the
Assume that the company in Problem 3.16 receives $800 for each item sold, (a) Express the company’s profit π as a function of the number x of items sold and evaluate the function at (b) x – 25
A company has a fixed cost of $8250 and a marginal cost of $450 for each item produced, (a)Express the cost C as a function of the number x of items produced and evaluate the function at (b) x= 20
(a) Use the algebra of functions to express the same farmer’s profit π as a function of the number x of bushels sold, and evaluate the function at (b) x = 20,000 and (c) x = 30,000. (a) (x) = R(x)
The farmer in Problem 3.13 has a fixed cost of $425,000 and a marginal cost of $15 a bushel, (a)Express his cost C as a function of the number x of bushels produced and estimate the function at (b)x
A farmer in a purely competitive market receives $35 a bushel for each bushel of wheat sold, (a)Express his revenue R as a function of the number x of bushels sold and evaluate the function at (b) x=
An office machine worth $12,000 depreciates in value by $1500 a year. Using linear or straight-line depreciation, express the value V of the machine as a function of years t. V(t) 12,000-1500
A potter exhibiting at a fair receives $24 for each ceramic sold minus a flat exhibition fee of $85.Express the revenue R he receives as a function of the number x of ceramics sold. R(x)=24x-85
An apple orchard charges $3.25 to enter and 60 cents a pound for whatever is picked. Express the cost C as a function of the number of pounds x of apples picked. C(x)=0.60x+3.25
A recording artist receives a fee of $9000 plus $2.75 for every album sold. Express her revenue R as a function of the number of albums x sold. R(x) 2.75x+9000 =
A plumber charges $50 for a house visit plus $35 an hour for each extra hour of work. Express the cost C of a plumber as a function of the number of hours x the job involves. C(x)=35x+50
Given f(x) = x4, g(x) = x2 – 3x + 4, andfind the following composite functions, as in Example 6. h(x) = x (x5) x-5
Givenuse the algebra of functions to find the following:(a) (f + h)(a)Substituting a for each occurrence of x, 3.x f(x): = x-4 g(x) = x+6 x+5 h(x) = x+1 x-2 (x -5,-1, 2)
Use the rules of the algebra of functions to combine the following functions by finding (1) (f + g)(x),(2) (f – g)(x), (3) (f · g)(x), and (4) (f ÷ g)(x). (a) f(x)=4x-5, g(x) = 7x - 3 (1)
In the graphs in Fig. 3-6, where y replaces f(x) as the dependent variable in functions, as is common in graphing, indicate which graphs are graphs of functions and which are not.From the definition
Parameters and other expressions can also be substituted into functions as the independent variable.Evaluate the following functions at the given values of x by substituting the various parameters
Evaluate the following functions at the given values of x.(a) f(x) = x2 – 4x + 7 at (1) x = 5, (2) x = −4 (1) Substituting 5 for each occurrence of x in the function,(2) Now substituting −4 for
Use the point-slope formula to derive the equation for each of the following straight lines: = (a) Passing through (2, 6), slope = 7 (c) Passing through (-10, 12), slope (d) Passing through (3, -11),
Derive the equation for a straight line having (a) Slope: -13, y intercept: (0, 22) (b) Slope: , y intercept: (0, -6) (c) Slope: -, y intercept: (0, 49) (d) Slope: 23.5, y intercept: (0, -70)
Find the x intercepts of each of the following equations in slope-intercept form: (a) y=7x+35 (b) y=-8x+64 (c) y=x-16- (d) y=-1.5x - 9
Find the x intercepts of the standard form equations below: (a) 6x13y = 126 (d) 13x+19y=-39 (b) x+17y=-8 (c) -5x-y=55
Find the y intercepts of each of the following equations in slope-intercept form: (a) y=-6.5x-23 (b) y=108x+14 (c) y 79.5x-250- (d) y=-3x + 0.65
Find the y intercepts of each of the following equations in standard form: (a) 8x-3y=15 (b) 13x + y = 4.5 (c) -26x + 7y = -56 (d) 47x18y = -9
Find the slopes of the lines passing through the following points: (a) (2, 7), (5, 19) (d) (9, 19), (15, 22) (b) (1, 9), (3, 3) (e) (-4, 0), (1, -3) (c) (3, 56), (7, 8) (f) (-7, 0), (-1, 0)
Find the slopes of the following linear equations: (a) y=-16x+23 (d) y = -x - 3 (b) y=x-9 (e) y = 19 (c) y 15.5x (f) x=27
Solve the following equations bv clearing the denominator: (4)3+8= (c) 240 x 2 - 22 22 (b) 5 4 = 576 675 = (d) = x+5 x+3 +8 120 375 x - -6 + x +3
Given that 0° (Celsius) is equal to 32°F (Fahrenheit) and 100°C is equal to 212°F and that there is a straight-line relationship between temperatures measured on the different scales, express the
Increasing at a constant rate, a company’s profits y have gone from $535 million in 1985 to $570 million in 1990. Find the expected level of profit for 1995 if the trend continues.Letting x = 0 for
Given two goods x and y with prices px and py and a budget B, (a) determine the slope-intercept form of the equation for the isocost curve. Using the information from (a), indicate what will happen
An isocost curve shows the different combinations of two goods that can be purchased with a given budget B. Blast furnaces can be heated with either gas (x) or coal (y). Given px = 100, py = 400, and
How much wine with an 18% alcohol content must be mixed with 6000 gallons of wine with a 12%alcohol content to obtain wine with a 16% alcohol content?Letting x = the amount of wine with 18% alcohol
A candy maker wants to blend candy worth 45 cents a pound with candy worth 85 cents a pound to obtain 200 pounds of a mixture worth 70 cents a pound. How much of each type should go into the
With $60,000 to invest, how much should a broker invest at 11 percent and how much at 15 percent to earn 14 percent on the total investment?If x = the amount invested at 11 percent, then (60,000 –
A retiree receives $5120 a year interest from $40,000 placed in two bonds, one paying 14 percent and the other 12 percent. How much is invested in each bond?Let x = the amount invested at 14 percent;
For tax purposes the value y of a computer after x years is y = 3,000,000 - 450,000.x Find (a) the value of the computer after 3 years, and (b) the salvage value after 5 (a) (b) y = 3,000,000
Find (a) the value after 6 years and (b) the salvage value after 8 years of a combine whose current value y after x years is (a) (b) y=67,500 7750x y=67,500 7750(6) = 21,000 y=67,500 7750(8) = 5500 -
Find the profit level of a firm in pure competition that has a fixed cost of $950, a variable cost of$70, and a selling price of $85 when it sells (a) 50 units and (b) 80 units. where R = 85x and C =
A firm operating in pure competition receives $45 for each unit of output sold. It has a variable cost of $25 per item and a fixed cost of $1600. What is its profit level π if it sells (a) 150
Find the total cost of producing (a) 20 units and (b) 35 units of output for a firm that has fixed costs of $3500 and a marginal cost of $400 per unit. (a) If x = 20, (b) If x = 35, C=400x + 3500
A firm has a fixed cost of $7000 for plant and equipment and a variable cost of $600 for each unit produced. What is the total cost C of producing (a) 15 and (b) 30 units of output? (a) If x = 15,
Verify the point-slope formula: yy =m(x-x1) For any point (x, y) to be on a line which passes through the point (x1,y) and has slope m, it must be true that - m= x-x1 Multiplying both sides of the
Prove the formula for the slope given in Section 2.4: y-y2 3 = X1 X2 Given two points (x, y) and (x2, y2) on the same line, both must satisfy the slope-intercept form of the equation: y = mx + b y2 =
Find the equations for the lines passing through the following points: (a) (3, 13) and (7,45) Using the two-point formula and the procedure demonstrated in Example 11, 32-yi 45 13 32 7-3 4 m= =8 then
Determine the equation for the line passing through (6, 4) and perpendicular to the line having the equation y = 2x + 15.Perpendicular lines have slopes that are negative reciprocals of one another.
Find the equation for the line passing through (−3, 6) and parallel to the line having the equation y =5x + 8.Parallel lines have the same slope. The slope of the line we seek therefore is 5.
Use the point-slope formula from equation (2.3) to derive the equation for each of the following: (a) Line passing through (3, 11), slope - 4. Taking the point-slope formula, y-ym(x-x1) and
Find the equation for the following straight lines with:(a) Slope = 7, y intercept: (0, 16)Using the slope-intercept form y = mx + b throughout, and substituting m = 7, b = 16 here,(b) Slope = −6,
Find the y intercepts and the x intercepts and use them as the two points needed to graph the following linear equations:(a) y = 5x + 10 y intercept: (0, 10), x intercept: (−2, 0). See Fig.
Use the information in Problem 2.11 to speed the process of finding the x intercepts for the following equations: (a) y 16x+64 Here m = 16, b = 64. Substituting in (2.7). (b) y 18x-9 With m 18, b =
Find the x intercept in terms of the parameters of the slope-intercept form of a linear equation y = mx+ b.Setting y = 0,The x intercept of the slope-intercept form is (−b/m, 0). 0 = mx + b mx = -b
Find the x intercept for the following equations:(a) y = 9x – 72 The x intercept is the point where the line crosses the x axis. Since the line crosses the x axis where y = 0, zero is the y
Find the y intercept for each of the following equations: (a) 5x+y=9 The y intercept occurs where the line crosses the y axis, which is the point where x = 0. Setting x = 0 in (a) above and solving
Use the different variations of the formula in Section 2.4 to find the slopes of the lines passing through the following points. Recall that the order in which you treat the points does not matter
To illustrate the steepness and direction conveyed by the slope, (a) draw five separate lines each with y intercept (0, 0) and having slopes of 1/4,1/2, 1,2, and 4 respectively; (b) draw five
Find the slopes of the lines of the following equations by first converting the equations to the slopeintercept form: (a) 24x+6y= 30 y = -4x+5 (c) 9x+y=-14 y=-18x-28 (e) 14x4y = 1 y=3x- m=-4 m=-18 m
Find the slopes of the lines of the following equations:In the slope-intercept form of a linear equation, the coefficient of x is the slope of the line. The slopes of the lines of the first four
Convert the following linear equations in standard form to the slope-intercept form by solving for y in terms of x.Note:1) If there is no constant term in the standard form of a linear equation as in
Plot the following points: (a) (3, 4), (b) (5, −2), (c) (−6, 3), (d) (0, −4), (e) (−7, 0), (f) (−8, −2), (g)(2, −3), (h) (−5, −4).(a) To plot (3, 4), move 3 units to the right of
Solve for x by clearing the denominator, that is, by multiplying both sides of the equation by the least common denominator (LCD) as soon as is feasible. (a) 15 x 4 XA Multiplying both sides of the
Use the properties of equality to solve the following linear equations by moving all terms with the unknown variable to the left, all other terms to the right, and then simplifying:With the equation
Estimate the following using a calculator: (a) 65 (f) 2197 (b) 37 (c) 8-4 (d) 12-6 (g) 50,625 (h) 7840.5 (e) 784 (i) 50,6250.25

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