# The function q = f(K; L) defined for K,L 0 is a production function for the firm.

hii…could anybody help me with this question:

The function q = f(K; L) defined for K,L > 0 is a production function for the firm. We do not have the specific form of the production function, but we know the following pieces of data:

• Currently the firm is employing 1 unit of labour and 1 unit of capital and producing 5 units of output.
• The MPL is currently 2 units, while the MPK is 3 units.
• The MPK declines at a constant rate of 0.2 , while the MPL diminish at a constant rate of 0.3.
• if capital is raised by 1 unit, while labour is held constant, this will increase the mpl by 0.24 of a unit.

Given the above information answer the following questions:

1. Evaluate the 1st order (Taylor) approximation for the level of output if the labour was increased by 0.5 from the current level, while the capital was increased by 1/3 from the current level.
2. Do you think that the 1st order approximation evaluated is over or under-estimates?
3. What is the slope of the isoquant of the production function at the point where K = 1 and L = 1? What is the economic interpretation of this value?