Consider a firm that utilizes Labor (L) and Capital (K) to produce a product Q, and the technology is given by the production function: Q = aL + bK. The wage rate of labor and the rental rate of capital are given by w and r respectively. (i) Draw the family of iso-quants and show that in a properly labelled diagram. (ii) Draw the iso-cost lines and show those in the same diagram. Note that the shape of these curves will depend on the parameter values of a, b, w and r. (iii) If the firm’s objective is to minimize cost of production, how should the two factors of production be combined in order to produce a given level of output in least costly manner? In other words, work out the cost minimizing input combinations.
Consider a firm that utilizes Labor (L) and Capital (K) to produce a product Q, and the technology is given
by the production function: Q = aL + bK. The wage rate of labor and the rental rate of capital are given by
w and r respectively.
(i) Draw the family of iso-quants and show that in a properly labelled diagram.
(ii) Draw the iso-cost lines and show those in the same diagram. Note that the shape of these
depend on the parameter values of a, b, w and r.
(iii) If the firm’s objective is to minimize cost of production, how should the two factors of production be
combined in order to produce a given level of output in least costly manner? In other words, work out
the cost minimizing input combinations.
(iv) Derive the cost function, the total cost of production as a function of output and draw the cost function.
(v) Can you find an interrelationship between the nature of the production function and that of the derived
cost function?
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