COFFEECONOMICS
80
REVISTA ACADÉMICA ECO (23) : 73-92, JULIO-DICIEMBRE DE 2020
4. The National Coffee Production Function model
The NCP-Function offers an alternative graphic and mathematical model to
analyze from a multi-dimensional perspective the final national output by country.
In fact, the NCP-Function offers policy makers, academics and central banks an
alternative methodological approach that allows them to measure the final output
of any country.
The NCP-Function is built by four sub-production functions as follows:
Sub-Production Function 0: Coffee Producers
☼
β0 = ƒ (
☼
∆α00,
☼
∆α01,
☼
∆α02,…,
☼
∆α0∞…)
(1)
Sub-Production Function 1: Coffee Brokers
☼
β1 = ƒ (
☼
∆α10,
☼
∆α11,
☼
∆α12,…,
☼
∆α1∞…)
(2)
Sub-Production Function 2: Sellers
☼
β2 = ƒ (
☼
∆α20,
☼
∆α21,
☼
∆α22,…,
☼
∆α2∞…)
(3)
Sub-Production Function 3: Coffee Consumers
☼
β3 = ƒ (
☼
∆α30,
☼
∆α31,
☼
∆α32,…,
☼
∆α3∞…)
(4)
☼ = Real Time
βi
= Output
∆
= Dynamic Growth Rate
All variables in each sub-production function require the application of the dynamic
growth rate, as follows:
☼
∆αij =
☼
∆αij <t+1> -
☼
∆αij<t0>/
☼
∆αij <t+1> x 100%
(5)
☼
∆αij<t0> i = {1,2,...,∞} and j = {1,2,...∞}
<t+1>
= Future time period
<to>
= Initial time period
Therefore, the final mathematical structure to build the NCP-Function is based on
Expression 6:
☼
β* ≡
☼
±β0
╬ ☼
±β1
╬
☼
±β2
╬
☼
±β3
(6)
╬ = linkage of quadrants
The Sub-Production Function 0 Specialization (Coffee Producer) shows a large
number of factors and functions that affect its behaviour simultaneously, according
to expressions 7, 8, 9, and 10.