A firm's production function is given as Q = 10L1/2 K1/2 where L and K are...

 

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A firm's production function is given as Q = 10L1/2 K1/2 where L and K are labour and capital. The firm's iso-cost function is C = wL + rK. (a) Using this production function, derive the short-run labour demand function, i.e. express the amount of labour employed by the firm as a function of the level of output it produces and the amount of capital it employs. (2marks) (b) Using your results from part (a), along with the iso-cost equation, determine the firm's short-run total cost function, assuming the price of capital, r, is $40, the price of labour, w, is $10, and the level of capital is held constant at 8 units. (2 marks) (c) Using your results from part (b), along with the fact that the firm's long-run cost function is LRTC = 4Q, determine the level of output, Q, at which the firm's short-run total cost is equal to its long-run total cost. Also, determine the optimal amount of labour that must be combined with the 8 units of capital to produce this level of output. (2marks) (d) Using your results from part (c), determine the values of short and long-run costs. (2marks) A firm's production function is given as Q = 10L1/2 K1/2 where L and K are labour and capital. The firm's iso-cost function is C = wL + rK. (a) Using this production function, derive the short-run labour demand function, i.e. express the amount of labour employed by the firm as a function of the level of output it produces and the amount of capital it employs. (2marks) (b) Using your results from part (a), along with the iso-cost equation, determine the firm's short-run total cost function, assuming the price of capital, r, is $40, the price of labour, w, is $10, and the level of capital is held constant at 8 units. (2 marks) (c) Using your results from part (b), along with the fact that the firm's long-run cost function is LRTC = 4Q, determine the level of output, Q, at which the firm's short-run total cost is equal to its long-run total cost. Also, determine the optimal amount of labour that must be combined with the 8 units of capital to produce this level of output. (2marks) (d) Using your results from part (c), determine the values of short and long-run costs. (2marks)