CHAPTER 19: Technology
MULTIPLE CHOICE
1. This problem will be easier if you have done Problem 1. A firm has the production function
$f(x1, x2) = x2.501x0.502. The isoquant on which output is 505/10 has the equation
a.
x2 = 50x−51.
b.
x2 = 50x21.
c.
x1/x2 = 5.
d.
x2 = 50x−0.501.
e.
x1 = 0.50x−0.502.
2. This problem will be easier if you have done Problem 1. A firm has the production function
$f(x1, x2) = 0.401x0.202. The isoquant on which output is 502/10 has the equation
a.
x2 = 50x51.
b.
x2 = 50x−0.201.
c.
x1/x2 = 2.
d.
x2 = 50x−21.
e.
x1 = 0.20x−0.802.
3. This problem will be easier if you have done Problem 1. A firm has the production function
$f(x1, x2) = 0.501x0.102. The isoquant on which output is 401/10 has the equation
a.
x1/x2 = 5.
b.
x2 = 40x101.
c.
x2 = 40x−51.
d.
x2 = 40x−0.101.
e.
x1 = 0.10x−0.902.
4. This problem will be easier if you have done Problem 1. A firm has the production function
$f(x1, x2) = x0.901x0.302. The isoquant on which output is 803/10 has the equation
a.
x2 = 80x3.331.
b.
x2 = 80x231.
c.
x1/x2 = 3.
d.
x2 = 80x−0.301.
e.
x1 = 0.30x−0.702.
5. This problem will be easier if you have done Problem 1. A firm has the production function
$f(x1, x2) = x11x0.502. The isoquant on which output is 805/10 has the equation
a.
x1/x2 = 2.
b.
x2 = 80x−0.501.
c.
x2 = 80x−21.
d.
x2 = 80x21.
e.
x1 = 0.50x−0.502
6. A firm has the production function f(x, y) = x1.40y1.90. This firm has
a.
decreasing returns to scale and diminishing marginal product for factor x.
b.
increasing returns to scale and decreasing marginal product for factor x.
c.
decreasing returns to scale and increasing marginal product for factor x.
d.
constant returns to scale.
e.
None of the above.
7. A firm has the production function f(x, y) = x1.20y2. This firm has
a.
constant returns to scale.
b.
decreasing returns to scale and increasing marginal product for factor x.
c.
increasing returns to scale and decreasing marginal product for factor x.
d.
decreasing returns to scale and diminishing marginal product for factor x.
e.
None of the above.
8. A firm has the production function f(x, y) = x1.40y1.40. This firm has
a.
constant returns to scale.
b.
decreasing returns to scale and increasing marginal product for factor x.
c.
decreasing returns to scale and diminishing marginal product for factor x.
d.
increasing returns to scale and decreasing marginal product for factor x.
e.
None of the above.
9. A firm has the production function f(x, y) = x1.10y1.30. This firm has
a.
decreasing returns to scale and diminishing marginal product for factor x.
b.
increasing returns to scale and decreasing marginal product for factor x.
c.
constant returns to scale.
d.
decreasing returns to scale and increasing marginal product for factor x.
e.
None of the above.
10. A firm has the production function f(x, y) = x1.10y1. This firm has
a.
constant returns to scale.
b.
decreasing returns to scale and diminishing marginal product for factor x.
c.
increasing returns to scale and decreasing marginal product for factor x.
d.
decreasing returns to scale and increasing marginal product for factor x.
e.
None of the above.
11. A firm uses 3 factors of production. Its production function is f(x, y, z) = minx3/y, y2, (z4 − x4)/y2. If
the amount of each input is multiplied by 6, its output will be multiplied by
a.
216.
b.
36.
c.
6.
d.
0.16.
e.
The answer depends on the original choice of x, y, and z.
12. A firm uses 3 factors of production. Its production function is f(x, y, z) = minx3/y, y2, (z4 − x4)/y2. If
the amount of each input is multiplied by 6, its output will be multiplied by
a.
6.
b.
36.
c.
0.16.
d.
216.
e.
The answer depends on the original choice of x, y, and z.
13. A firm uses 3 factors of production. Its production function is f(x, y, z) = minx4/y, y3,(z5 − x5)/y2. If
the amount of each input is multiplied by 5, its output will be multiplied by
a.
0.04.
b.
125.
c.
625.
d.
25.
e.
The answer depends on the original choice of x, y, and z.
14. A firm uses 3 factors of production. Its production function is f(x, y, z) = minx5/y, y4,(z6 − x6)/y2. If
the amount of each input is multiplied by 3, its output will be multiplied by
a.
81.
b.
27.
c.
243.
d.
0.04.
e.
The answer depends on the original choice of x, y, and z.
15. A firm uses 3 factors of production. Its production function is f(x, y, z) = minx4/y, y3,(z5 − x5)/y2. If
the amount of each input is multiplied by 2, its output will be multiplied by
a.
8.
b.
4.
c.
16.
d.
0.22.
e.
The answer depends on the original choice of x, y, and z.
16. A firm has a production function f(x, y) = 1.80(x0.10 + y0.10)2 whenever x 0 and y 0. When the
amounts of both inputs are positive, this firm has
a.
increasing returns to scale.
b.
decreasing returns to scale.
c.
constant returns to scale.
d.
increasing returns to scale if x + y 1 and decreasing returns to scale otherwise.
e.
increasing returns to scale if output is less than 1 and decreasing returns to scale if output
is greater than 1.
17. A firm has a production function f(x, y) = 0.70(x0.80 + y0.80)2 whenever x 0 and y 0. When the
amounts of both inputs are positive, this firm has
a.
increasing returns to scale if x + y 1 and decreasing returns to scale otherwise.
b.
increasing returns to scale.
c.
decreasing returns to scale.
d.
constant returns to scale.
e.
increasing returns to scale if output is less than 1 and decreasing returns to scale if output
is greater than 1.
18. A firm has a production function f(x, y) = 1.80(x0.80 + y0.80)1 whenever x 0 and y 0. When the
amounts of both inputs are positive, this firm has
a.
increasing returns to scale.
b.
constant returns to scale.
c.
decreasing returns to scale.
d.
increasing returns to scale if x + y 1 and decreasing returns to scale otherwise.
e.
increasing returns to scale if output is less than 1 and decreasing returns to scale if output
is greater than 1.
19. A firm has a production function f(x, y) = 2(x0.90 + y0.90)5 whenever x 0 and y 0. When the amounts
of both inputs are positive, this firm has
a.
increasing returns to scale if x + y 1 and decreasing returns to scale otherwise.
b.
increasing returns to scale.
c.
decreasing returns to scale.
d.
constant returns to scale.
e.
increasing returns to scale if output is less than 1 and decreasing returns to scale if output
is greater than 1.
20. A firm has a production function f(x, y) = 0.70(x0.20 + y0.20)4 whenever x 0 and y 0. When the
amounts of both inputs are positive, this firm has
a.
increasing returns to scale.
b.
decreasing returns to scale.
c.
constant returns to scale.
d.
increasing returns to scale if x + y 1 and decreasing returns to scale otherwise.
e.
increasing returns to scale if output is less than 1 and decreasing returns to scale if output
is greater than 1.
21. In Problem 3, if the exponents in the production function were 0.30 for x1 and 0.30 for x2, this
production function would exhibit (constant, increasing, decreasing) returns to scale and (would,
would not) have diminishing technical rate of substitution.
a.
constant, would
b.
constant, would not
c.
decreasing, would not
d.
increasing, would
e.
decreasing, would
22. In Problem 3, if the exponents in the production function were 0.30 for x1 and 0.20 for x2, this
production function would exhibit (constant, increasing, decreasing) returns to scale and (would,
would not) have diminishing technical rate of substitution.
a.
decreasing, would not
b.
constant, would not
c.
increasing, would
d.
constant, would
e.
decreasing, would
23. In Problem 3, if the exponents in the production function were 0.80 for x1 and 0.20 for x2, this
production function would exhibit (constant, increasing, decreasing) returns to scale and (would,
would not) have diminishing technical rate of substitution.
a.
constant, would
b.
decreasing, would not
c.
increasing, would
d.
constant, would not
e.
decreasing, would
24. In Problem 3, if the exponents in the production function were 0.60 for x1 and 0.40 for x2, this
production function would exhibit (constant, increasing, decreasing) returns to scale and (would,
would not) have diminishing technical rate of substitution.
a.
constant, would not
b.
increasing, would
c.
decreasing, would not
d.
constant, would
e.
decreasing, would
25. In Problem 3, if the exponents in the production function were 0.40 for x1 and 0.40 for x2, this
production function would exhibit (constant, increasing, decreasing) returns to scale and (would,
would not) have diminishing technical rate of substitution.
a.
increasing, would
b.
decreasing, would not
c.
constant, would
d.
constant, would not
e.
decreasing, would
26. In Problem 8, if a = 2.50, b = 0.60, and c = 1, the marginal products of x1, x2, and x3 (in this order) are
a.
increasing, decreasing, and constant.
b.
decreasing, increasing, and decreasing.
c.
all increasing.
d.
all decreasing.
e.
all increasing if A 1.
27. In Problem 8, if a = 2.40, b = 0.50, and c = 1, the marginal products of x1, x2, and x3 (in this order) are
a.
increasing, decreasing, and constant.
b.
all increasing.
c.
all decreasing.
d.
decreasing, increasing, and decreasing.
e.
all increasing if A 1.
28. In Problem 8, if a = 2.10, b = 0.90, and c = 1, the marginal products of x1, x2, and x3 (in this order) are
a.
decreasing, increasing, and decreasing.
b.
all increasing.
c.
increasing, decreasing, and constant.
d.
all decreasing.
e.
all increasing if A 1.
29. In Problem 8, if a = 2.10, b = 0.40, and c = 1, the marginal products of x1, x2, and x3 (in this order) are
a.
all decreasing.
b.
increasing, decreasing, and constant.
c.
decreasing, increasing, and decreasing.
d.
all increasing.
e.
all increasing if A 1.
30. In Problem 8, if a = 2.10, b = 1.10, and c = 1.20, the marginal products of x1, x2, and x3 (in this order)
are
a.
all increasing.
b.
decreasing, increasing, and decreasing.
c.
all decreasing.
d.
increasing, decreasing, and constant.
e.
all increasing if A 1.