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Calculate the firm optimal choice of capital and labour

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A firm chooses between capital, K, and labour, L, in order to produce a given level of output, q. Capital incurs a capital rental rate, r, and labour incurs a wage rate, w. The firm's associated cost minimisation problem can be characterised by the Lagrangian function, denoted by La, below.

?la=5L+10K-λ((2K0.5+2L0.5-q)?

K AND l ARE TO THE POWER OF 0.5

a) By inspection of this function, provide an expression for:

i) The firm's production function

ii) The value of the wage rate, w

b) State the three first order conditions that follow from the Lagrangian.

c) Hence, calculate the firm's optimal choice of capital and labour as a function of output, q. Show all your working.

Reference no: EM132526596

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