1. Consider the following production functions

q = L + K q = L K q = L + L K + K

a) Compute the marginal and average productivity functions of labour and capital for the above functions.

b) How would you explain the law of diminishing marginal productivity?

2. Further to Question 1, answer the following.

a) Under what conditions do the functions in Question 1 exhibit decreasing returns to scale, constant returns to scale, or increasing returns to scale? b) Compute the marginal rate of technical substitution of the above functions.

3. A firm finds that its production function is of the Cobb-Douglas form:

q = 100L^0.25 K ^0.75

where q is weekly output (in tonnes)

and L and K are weekly inputs of worker-hours and machine-hours respectively.

a) Find the equation of the isoquant for q = 100.

b) Give an economic interpretation to the slope and curvature of the isoquant.

c) Would other isoquants for this production function have a similar shape?