A firm sells its output in a perfectly competitive market at a fixed price of $10 per unit. it buys tow imputs L and K at prices of $15 per unit and $50 per unit respectively and has following production function: Q=100L^0.3K^0.5.
a. Use calculus to show that the production function exhibits diminishing returns to labor. interpret your answer.
b. Now show that if the same production function also has diminishing returns to capital.
c. Are the return to captial and labor the same? brefly explain your answer.