Question 1 Show your working.
(a) (i) Find the first-order and second-order partial derivatives for the utility function
(ii) For the benefit of someone who is neither a mathematician nor an economist, explain what
information is provided by each of the derivatives which involves differentiation with respect to x. (There is no need to define utility.)
(iii) Are the marginal functions increasing or decreasing. Justify your answers.
(b) Consider the production function, .
(i) Show whether it has increasing, decreasing or constant returns to scale.
(ii) Does it exhibit diminishing returns to labour? Explain.