(a) A competitive firm has a production function described as follows. "Weekly output is the square root of the minimum of the number of units of capital and the number of units of labour employed per week." Suppose that in the short run this firm must use 16 units of capital but can vary its amount of labour freely.

i. Write down a formula that describes the marginal product of labour in the short run as a function of the amount of labour used. (Be careful at the boundaries.)

ii. If the wage is w = $1 and the price of output is p = $4, how much labour will the firm demand in the short run?

iii. What if w = $1 and p = $10?

iv. Write down an equation for the firm's short-run demand for labour as a function of w and p.