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.

Do a little research, then take a shot. What do you think?

Hint: raise both S and H by some percentage (say 10%). Does TC rise by:
a) more than 10% (dis-economies of scope)
b) less than 10% (economies of scope), or
c) exactly 10% (zero economies of scope)

To analyze whether there are economies of scope in the production of hardware (H) and software (S), we need to understand what economies of scope mean in this context.

Economies of scope refer to cost savings generated from producing multiple products together rather than separately. In other words, it is the cost advantage gained when producing different products together compared to producing each product individually.

To determine if economies of scope exist, we need to examine the total cost equation and analyze how the different cost components interact.

The given total cost equation is:
TC = aS + bH - dSH

Let's break down the different terms in the equation:

- aS: This represents the cost associated with producing software (S). The coefficient 'a' reflects the unit cost per unit of software produced.

- bH: This represents the cost associated with producing hardware (H). The coefficient 'b' reflects the unit cost per unit of hardware produced.

- dSH: This term represents the interdependencies (interaction) between software (S) and hardware (H) production. The coefficient 'd' represents the strength of the interaction.

Now, let's consider the possibilities:

1. If d is positive:
If the coefficient 'd' is positive, it indicates a positive interaction between producing software (S) and hardware (H). In this case, as the production of one product increases, it leads to a decrease in the cost of producing the other product. This demonstrates economies of scope, indicating that producing both hardware and software together results in cost savings.

2. If d is negative:
If the coefficient 'd' is negative, it indicates a negative interaction between producing software (S) and hardware (H). In this case, as the production of one product increases, it leads to an increase in the cost of producing the other product. This suggests diseconomies of scale, meaning producing both hardware and software together results in additional costs.

3. If d is zero:
If the coefficient 'd' is zero, it means there is no interaction between producing software (S) and hardware (H). In this case, the cost of producing each product is independent of the other. Therefore, there are no economies of scope.

To determine whether there are economies of scope, it is necessary to know the value of the coefficient 'd'. Once the value of 'd' is known, we can analyze the sign (positive or negative) to determine the presence or absence of economies of scope in the production of hardware and software.