Answer to Question #58167 in Microeconomics for Lauren
PL = $6, PK = $9.
In microeconomic theory, the Marginal Rate of Technical Substitution (MRTS) is the amount by which the quantity of one input has to be reduced when one extra unit of another input is used, so that output remains constant.
The firm's marginal rate of technical substitution will be:
MRTS = MPL/MPK = (10(K/L)^0.5) / ((10(L/K)^0.5) = (K/L)^0.5 / (L/K)^0.5 = (K/L)^0.5*(K/L)^0.5 = K/L
In this case the highest amount of output is produced, when K = L, so 6L + 9K = 300,
6L + 9L = 300,
15L = 300
L = K = 20 units.
Q = 20*20^0.5*20^0.5 = 400 iPods.
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Supppose that a farm's production function is determined by two factors: land area (K) and labour (L). The
production function is specified as follows:
Q = 64K^0.5 L^>5
The farm's land area is 500 acres
The unit cost of capital and labour is as follows:
- land $10 per acre
- labour $500 per labour