Question

2.(15 points) A firm uses capital and labor in its production process. Capital is fixed in the short run while labor is variable. Assume that the firm has acquired the optimal quantity of capital for the production of 100 units of output. Using typically shaped isoquants and isocost lines, demonstrate that the cost to the firm of increasing output to 200 units will be greater in the short run than in the long run. Identify the short-run expansion path and the long-run expansion path.

Answer 1

ĶI - 202 -Q=100 L2 Initially when 92100, the equilibrium is at A whi with K* and 2* inputs. Now, if in short reen the 9 is to be doubled to 200, the capital is fixed, hence the only way to increase q to 200 is beg increasing the Labour input. Keeping capital constant and increasing the Labour input would lead to diminishing returns in terms of Labour, hence more of labour is used which has reduced efficiency. Thus it is not the optimum solution as more of labour is used which leads to loss of efficiency of labour. On the other hand, if we consider long run where both can be increased to attain q=200, both labour and capital will be increased in the same ratio which will not lead to DRS and the solution will be optimum and cost efficient. C will be long reen equilibrium

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