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Efficient allocation of resources

Suppose that the production of crayons q is conducted at 2 locations and uses only labor as an input. The production function in location 1 is given by q1=10L1 1/2(exponent) and location 2 by q2=50 L2 1/2(exponent).

a. If a single firm produces crayons in both locations, then it will obviously want to get as large an output as possible given the labor input it uses. How should it allocate labor between the locations in order to do so? Explain precisely the relationship between L1 and L2.

b. Assuming that the firm operates in the efficient manner described in part A, how does total output Q depend on the total amount of labor hired (L)?

Solution Preview

a. If a single firm produces crayons in both locations, then it will obviously want to get as large an output as possible given the labor input it uses. How should it allocate labor between the locations in order to do so? Explain precisely the relationship between L1 and L2.

Location 1
q1=10L1^(1/2)
Marginal product of labor at location 1 (MP1)
=dq1/dL1
=1/2*10*L1^(-1/2)
=5L1^(-1/2)

Let Price of crayon be P per unit.
Marginal Revenue product at ...

Solution Summary

Solution describes the methodology to allocate labor between two production locations. It also determines relationship between total output and total labor hired.

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