Suppose that the production of crayons (q) is conducted at two locations and use
ID: 1254255 • Letter: S
Question
Suppose that the production of crayons (q) is conducted at two locations and uses only labor as an input.The production function in location 1 by Q1=10Lx^0.5 and in location 2 by Q2=50Ly^0.5
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 Lx and Ly.
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)?
Explanation / Answer
a) total quantity produced = Q1 +Q2 = q = 10Lx^0.5 + 50Ly^0.5 now to maximize this we take d(Q1 +Q2)/dLx = 5Lx^-.5 simillarly we get Dq/dLy if Lx=Ly Q1/Q2 = 1/5 for optimization we adjust (Lx/Ly)^.5 = 5/1 for max output and minimum labor (Lx/Ly)^.5 = 5 ANSWER b) = Q1 +Q2 = q = 10Lx^0.5 + 50Ly^0.5 using (Lx/Ly)^.5 = 5 Lx= 25Ly Q1 +Q2 = q = 10(25Ly)^0.5 + 50Ly^0.5 = 100Ly^.5 or 20Lx^.5 ANSWER PLEASE RATE
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