Economists uses many tools to determine productivity and economic growth. One of these tools is the aggregate production function. It converts the inputs of economics such as labor and raw materials into a formula with the output of the products or services produced. Specifically, the Cobb-Douglas production function is the formula used for this calculation.
Use the Cobb-Douglas function to determine total aggregate production. The formula is given as production is equal to real output per input unit (sometimes simplified to "technology") times labor input times capital input or Y = A X L^a X K^b. Exponential a and b are less than one and indicate loss of productivity in transferring to an aggregate value.
Find the three variables in the formula. A is a scalar variable that depends on the other two numbers. It is the real output for the value of work and capital that is invested into a project.
Assume capital is $1 million, labor is 5,000 hours and output value is $200 per unit. The exponential a and b are each 0.5.
Insert the values for the variables and solve for aggregate production: Y = A X L^a X K^b Y = 200 X 5,000^.5 X 1,000,000^.5 Y = $14,142,135