A computer company produces hardware and software using the same facility. (i.e., with the same L and K). The total cost of producing software (S) and hardware (H) equals:
TC = a S + b H - d S H,
where a, b, and d are positive constants. Are there economies of scope in the production of H and S? Explain why or why not.
see my earlier posts to this very question.
To determine if there are economies of scope in the production of hardware (H) and software (S), we need to analyze how the cost changes when they are produced together compared to when they are produced separately.
The equation provided to calculate the total cost of production is:
TC = aS + bH - dSH
For economies of scope to exist, the joint production of H and S should result in a lower total cost compared to producing them separately.
To check for economies of scope, we need to compare the total cost of producing them together (TC) with the sum of the costs of producing them separately (TC_H and TC_S).
Let's calculate the total cost when producing H and S separately:
TC_H = bH
TC_S = aS
Now, let's calculate the total cost of producing them together:
TC = aS + bH - dSH
If TC_H + TC_S > TC, then there are economies of scope because producing them together is cheaper. Conversely, if TC_H + TC_S < TC, there are diseconomies of scope.
Since you haven't provided specific values for a, b, and d, I can't perform the exact calculations. However, you can fill in the specific values and compare the costs yourself.
If the resulting equation shows that TC_H + TC_S is greater than TC, then there are economies of scope in the production of H and S. This implies that producing hardware and software together reduces costs and is more efficient than producing them separately.