Multiplier principle. Suppose that Congress enacts a one-time-only 10% tax rebate that is expected to infuse $ y billion, 5 ≤ y ≤ 7, into the economy. If every person and every corporation is expected to spend a proportion x, 0.6 ≤ x ≤ 0.8, of each dollar received, then, by the multiplier principle in economics, the total amount of spending S (in billions of dollars) generated by this tax rebate is given by S ( x , y ) = y 1 − x What is the average total amount of spending for the indicated ranges of the values of x and y ? Set up a double integral and evaluate it.
Multiplier principle. Suppose that Congress enacts a one-time-only 10% tax rebate that is expected to infuse $ y billion, 5 ≤ y ≤ 7, into the economy. If every person and every corporation is expected to spend a proportion x, 0.6 ≤ x ≤ 0.8, of each dollar received, then, by the multiplier principle in economics, the total amount of spending S (in billions of dollars) generated by this tax rebate is given by S ( x , y ) = y 1 − x What is the average total amount of spending for the indicated ranges of the values of x and y ? Set up a double integral and evaluate it.
Solution Summary: The author calculates the average total amount of spending for the indicated ranges of the values of x and y.
Multiplier principle. Suppose that Congress enacts a one-time-only 10% tax rebate that is expected to infuse $y billion, 5 ≤ y ≤ 7, into the economy. If every person and every corporation is expected to spend a proportion x, 0.6 ≤ x ≤ 0.8, of each dollar received, then, by the multiplier principle in economics, the total amount of spending S (in billions of dollars) generated by this tax rebate is given by
S
(
x
,
y
)
=
y
1
−
x
What is the average total amount of spending for the indicated ranges of the values of x and y? Set up a double integral and evaluate it.
sy = f(x)
+
+
+
+
+
+
+
+
+
X
3
4
5
7
8
9
The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open
interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem
and the Mean Value Theorem for f on the closed interval [0, 9] ?
(A
A
B
B
C
D
=
Q6 What will be the allowable bearing capacity of sand having p = 37° and ydry
19 kN/m³ for (i) 1.5 m strip foundation (ii) 1.5 m x 1.5 m square footing and
(iii)1.5m x 2m rectangular footing. The footings are placed at a depth of 1.5 m
below ground level. Assume F, = 2.5. Use Terzaghi's equations.
0
Ne
Na
Ny
35 57.8 41.4 42.4
40 95.7 81.3 100.4
Q1 The SPT records versus depth are given in table below. Find qan for the raft 12%
foundation with BxB-10x10m and depth of raft D-2m, the allowable
settlement is 50mm.
Elevation, m 0.5 2
2 6.5 9.5 13 18 25
No.of blows, N 11 15 29 32 30 44
0
estigate shear
12%
Chapter 7 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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