Question #53226

A detailed solution i.e with working for the below question:
Q: For the production function Q=20K^0.5 L^0.5, determine four combination of capital and labor that will produce 100 and 200 units of output. Plot these points on a graph and use them to sketch the 100 and 200 unit isoquants.
Ans: If the production function is Q=20K^0.5 L^0.5, then four combination of capital and labor that will produce 100 and 200 units of output will be (K;L):
Q = 100 units: (1;25), (25;1), (6.25;2), (2;6.25);
Q = 200 units: (1;100), (100;1), (25;2), (2;25).

Expert's answer

If the production function is Q=20K^0.5 L^0.5, then four combination of capital and labor that will produce 100 and 200 units of output will be (K;L):

K = Q^2/400L, so if Q = 100, then K = 25/L

Q = 100 units: (1;25), (25;1), (6.25;2), (2;6.25);

Because, for example, 20*1^0.5*25^0.5 = 20*1*5 = 100 units.

K = Q^2/400L, so if Q = 200, then K = 100/L

Q = 200 units: (1;100), (100;1), (25;2), (2;25).

K = Q^2/400L, so if Q = 100, then K = 25/L

Q = 100 units: (1;25), (25;1), (6.25;2), (2;6.25);

Because, for example, 20*1^0.5*25^0.5 = 20*1*5 = 100 units.

K = Q^2/400L, so if Q = 200, then K = 100/L

Q = 200 units: (1;100), (100;1), (25;2), (2;25).

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