Answer:
Explanation:
The purpose of allocating the output of the shoes is to diminish the total cost of production. The process is achieved by assigning a pair of shoes that requires production at the factory with a marginal lower cost of the two plants. Afterward, the firms will have to equate the marginal cost of production across the two firms.
For firm 1:
The cost of production
Differentiating with respect to to determine the marginal cost;
For firm 1, the Marginal cost
For firm 2; the marginal cost
Equating both from above:
Recall that:
Thus, we can replace the value of into the above equation to determine the value of
in terms of
by applying a quadratic formula.
Assuming we knew the values of we can estimate the numerical value of
, then replace it into the equation
to find the numerical value for
.