The firm will hire labor and capital up to the point where:
From the given production function, the marginal product of labor is:
And the marginal product of capital is:
The price of labor is W = R5. and the price of capital is r = R42 Therefore:
"\\dfrac{K}{L} = \\dfrac{1}{7}"
Solving for L and K each at a time, we get:
Substituting equations (i) and (ii) into the production function each at a time:
"q = 1.729L^{0.55}""\\color{red}{L^* \\approx 0.37q^{20\/11}}"
"q = 3.1K^{0.55}"
"\\color{red}{K^* \\approx 0.13q^{20\/11}}"
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