All figure titles and notes are outside of the figures themselves. The title directly above a figure, and the note
directly below, belong to that figure.
Figure 1: The London Times 1815-1991
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1815 1825 1835 1845 1855 1865 1875 1885 1895 1905 1915 1925 1935 1945 1955 1965 1975 1985 1991
Figure 2: The New York Times 1861-2011
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1861
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1991
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2011
Figure 3: Proposition 2, Part (i)
0.3
0.2
∗
𝑒𝑊
𝑒𝐹∗
0.1
0
0.1
0.6
1.1
1.6
2.1
2.6
𝑢W
∗
Note.—Figure is based on the numerical example in the last paragraph of Section 4, with 𝑒𝐹∗ and 𝑒𝑊
defined by equations (1) and (2). Parameters are fixed at the following values: =1, =0.4, aF=1, aW=2,
uF=1, n=10, F =30, W =4.
Figure 4: Proposition 2, Part (ii)
0.5
0.4
0.3
0.2
∗
𝑒𝑊
𝑒𝐹∗
0.1
0
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
2.3
2.5
2.7
2.9
𝑢F
∗
Note.—Figure is based on the numerical example in the last paragraph of Section 4, with 𝑒𝐹∗ and 𝑒𝑊
defined by equations (1) and (2). Parameters are fixed at the following values: =1, =0.4, aF=1, aW=2,
uW=1, n=5, F=30, W=4.
Figure 5: Proposition 2, Part (iii)
0.4
0.3
0.2
∗
𝑒𝑊
𝑒𝐹∗
0.1
0
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5 11.5 12.5 13.5 14.5
𝒏
∗
Note.—Figure is based on the numerical example in the last paragraph of Section 4, with 𝑒𝐹∗ and 𝑒𝑊
defined by equations (1) and (2). Parameters are fixed at the following values: =1, =0.2, aF=1, aW=2,
uF=1, uW=6, F=30, W=4.
Figure 6: Proposition 2, Part (iv)
0.6
0.5
0.4
0.3
∗
𝑒𝑊
𝑒𝐹∗
0.2
0.1
0
1.5
2.25
3
3.75
4.5
5.25
6
6.75
7.5
8.25
W
∗
Note.—Figure is based on the numerical example in the last paragraph of Section 4, with 𝑒𝐹∗ and 𝑒𝑊
defined by equations (1) and (2). Parameters are fixed at the following values: =1, =0.2, aF=1, aW=2,
uF=1, n=5, F=30, uW=4.
Figure 7: Proposition 2, Part (v)
0.6
0.5
0.4
0.3
∗
𝑒𝑊
0.2
𝑒𝐹∗
0.1
0
16.5
19
21.5
24
26.5
29
F
∗
Note.—Figure is based on the numerical example in the last paragraph of Section 4, with 𝑒𝐹∗ and 𝑒𝑊
defined by equations (1) and (2). Parameters are fixed at the following values: =1, =0.4, aF=1, aW=2,
uF=1, n=10, uW=1, W=4.