Which among the firms C, D, E, and F had the least amount of R & D spending per employee in 2023?

Firm	ES '19	PAT '19	PRD '19	ES '23	PAT '23	PRD '23
A	40	20	4
B	35	25	5
C	25	30	9
D	55	35	6
E	20	10	6
F	65	55	7

Firm	$PAT_{23}/PAT_{19}$	PAT/ES '23	R&D '23	R&D/ES '23
A
B
C
D
E
F

The 2019 plot is read off (x = ES, y = PAT, marker area = PRD). The values above are the approximate readings; for most questions only the relative positions matter.

Note that E sits lowest on the PAT axis in 2019 (PAT $=10$) and C carries one of the largest markers (PRD $=9$).

Firm	ES '19	PAT '19	PRD '19	ES '23	PAT '23	PRD '23
A	40	20	4	50	30	5
B	35	25	5	40	45	6
C	25	30	9	20	60	2
D	55	35	6	60	40	3
E	20	10	6	30	50	7
F	65	55	7	70	70	8

Firm	$PAT_{23}/PAT_{19}$	PAT/ES '23	R&D '23	R&D/ES '23
A
B
C
D
E
F

The 2023 plot is read off the same way. Note C has climbed to a high PAT ($60$) while its marker has shrunk to a small PRD ($2$), and it sits at a low ES ($20$).

Firm	ES '19	PAT '19	PRD '19	ES '23	PAT '23	PRD '23
A	40	20	4	50	30	5
B	35	25	5	40	45	6
C	25	30	9	20	60	2
D	55	35	6	60	40	3
E	20	10	6	30	50	7
F	65	55	7	70	70	8

Firm	$PAT_{23}/PAT_{19}$	PAT/ES '23	R&D '23	R&D/ES '23
A	1.50
B	1.80
C	2.00
D	1.14
E	5.00
F	1.27

The PAT growth ratios are filled in: $30/20$, $45/25$, $60/30$, $40/35$, $50/10$, $70/55$.

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Since ARG is constant and the window 2019 to 2023 is the same 4 years for every firm, $PAT_{2023}=PAT_{2019}(1+ARG)^4$. A larger ratio $PAT_{23}/PAT_{19}$ therefore means a larger ARG. E stands out with $5.00$.

Firm	ES '19	PAT '19	PRD '19	ES '23	PAT '23	PRD '23
A	40	20	4	50	30	5
B	35	25	5	40	45	6
C	25	30	9	20	60	2
D	55	35	6	60	40	3
E	20	10	6	30	50	7
F	65	55	7	70	70	8

Firm	$PAT_{23}/PAT_{19}$	PAT/ES '23	R&D '23	R&D/ES '23
A	1.50	0.60
B	1.80	1.13
C	2.00	3.00
D	1.14	0.67
E	5.00	1.67
F	1.27	1.00

PAT per employee in 2023 is filled in as $PAT_{23}/ES_{23}$: $30/50$, $45/40$, $60/20$, $40/60$, $50/30$, $70/70$. C is clearly the highest at $3.00$ because of its high PAT on a small workforce.

Firm	ES '19	PAT '19	PRD '19	ES '23	PAT '23	PRD '23
A	40	20	4	50	30	5
B	35	25	5	40	45	6
C	25	30	9	20	60	2
D	55	35	6	60	40	3
E	20	10	6	30	50	7
F	65	55	7	70	70	8

Firm	$PAT_{23}/PAT_{19}$	PAT/ES '23	R&D '23	R&D/ES '23
A	1.50	0.60	1.5
B	1.80	1.13	2.7
C	2.00	3.00	1.2
D	1.14	0.67	1.2
E	5.00	1.67	3.5
F	1.27	1.00	5.6

R&D spend in 2023 is computed as $PAT_{23}\times\frac{PRD_{23}}{100}$: e.g. C $=60\times0.02=1.2$, D $=40\times0.03=1.2$, E $=50\times0.07=3.5$, F $=70\times0.08=5.6$.

Firm	ES '19	PAT '19	PRD '19	ES '23	PAT '23	PRD '23
A	40	20	4	50	30	5
B	35	25	5	40	45	6
C	25	30	9	20	60	2
D	55	35	6	60	40	3
E	20	10	6	30	50	7
F	65	55	7	70	70	8

Firm	$PAT_{23}/PAT_{19}$	PAT/ES '23	R&D '23	R&D/ES '23
A	1.50	0.60	1.5	0.030
B	1.80	1.13	2.7	0.068
C	2.00	3.00	1.2	0.060
D	1.14	0.67	1.2	0.020
E	5.00	1.67	3.5	0.117
F	1.27	1.00	5.6	0.080

R&D per employee in 2023 is R&D '23 divided by ES '23: C $=1.2/20=0.060$, D $=1.2/60=0.020$, E $=3.5/30=0.117$, F $=5.6/70=0.080$. D is the smallest because the same R&D amount as C is spread over a much larger workforce.

Firm	ES '19	PAT '19	PRD '19	ES '23	PAT '23	PRD '23
A	40	20	4	50	30	5
B	35	25	5	40	45	6
C	25	30	9	20	60	2
D	55	35	6	60	40	3
E	20	10	6	30	50	7
F	65	55	7	70	70	8

Firm	$PAT_{23}/PAT_{19}$	PAT/ES '23	R&D '23	R&D/ES '23
A	1.50	0.60	1.5	0.030
B	1.80	1.13	2.7	0.068
C	2.00	3.00	1.2	0.060
D	1.14	0.67	1.2	0.020
E	5.00	1.67	3.5	0.117
F	1.27	1.00	5.6	0.080

Last, the 2018 figure needed for C. Using its ARG, $(1+r)^4 = 60/30 = 2$, so $1+r = 2^{1/4}\approx1.189$.

Going one year before 2019: $PAT_{2018}=\frac{PAT_{2019}}{1+r}=\frac{30}{1.189}\approx25.2$.

The only PRD reading available near 2018 is the 2019 marker, $9\%$, so $R\&D_{2018}\approx25.2\times0.09\approx2.27$.

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All raw readings and derived quantities are now populated. The values are graph readings, so small rounding differences are expected; the comparative orderings are robust: ARG ordering led by E, PAT/employee in 2023 led by C, and R&D/employee in 2023 lowest for D.

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R&D per employee in 2023 is $\frac{PAT_{2023}\times PRD_{2023}/100}{ES_{2023}}$. For the four firms asked:

• C: $\frac{60\times0.02}{20}=\frac{1.2}{20}=0.060$
• D: $\frac{40\times0.03}{60}=\frac{1.2}{60}=0.020$
• E: $\frac{50\times0.07}{30}=\frac{3.5}{30}\approx0.117$
• F: $\frac{70\times0.08}{70}=\frac{5.6}{70}=0.080$

D has the same total R&D as C ($1.2$) but spread over a much larger workforce ($60$ vs $20$), giving the smallest value, $0.020$. Hence the least R&D spending per employee is Firm D, option 2.