Question

1. A firm's marginal product of labor is 4 and its marginal product of capital is 5. If the firm adds one unit of labor, but does not want its output quantity to change, how many more or less units of capital the firm should use?

2. A firm has the production function ? = ?(?₁, ?₂) = ?₁^0.5 ?₂².

   1. Does this firm have an increasing or decreasing return to scale? Why?

   2. Does this firm have increasing or decreasing marginal product for the two input factors?

      Why?

Answer 1

The marginal product of labour is 4. this implies that if there is one more worker added then the output increases by 4 units. However if we reduce the capital usage by 4/5 = 0.8 units, output will decline by 5*0.8 = 4 units. This will indicate that there is no change in the output even though the capital usage has decreased and labour usage has increased. Therefore capital should be reduced by 0.8 units

the sum of the exponent of inputs is 2.5 which is greater than 1 and therefore there are increasing returns to scale. The marginal product of x1 is negative which means they are diminishing marginal returns for x1. however marginal product of X2 is positive which means there are increasing returns for X2