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