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.