5- One way economists measure total factor productivity is to use a Cobb-Douglas production function of the form where A denotes technical progress and a the relative importance of capital input. Taking natural logarithms of this production function yields Inq lnA + a In K + (1 a) In L (8) One useful property of natural logarithms is that the change in Inx is approximately equal to the percentage change in X itself. Roughly speaking, AlnX is a proxy for %AX, or In this course, you may ignore small differences. It is the result of ceteris paribus assumption. This problem can be solved using partial derivatives which will be used in more advanced courses. a. b. o,'odq z + a%AK+ (1 Explain how this would allow you to calculate annual changes in the technical change factor (e.g. %AA) from the knowledge of changes in q, K, and L and of the parameter a. The average product of labour, i.e. q/' is commonly known as labour productivity. Use the results from part b to show that the percentage increase in labour productivity can be decomposed to change in A (technical progress) and increase in the capital-labour ratio, i.e. K/L, which is known as capital deepening, or 0/0A %AA+ Hint: Subtract In L from both sides of Remember In In X Iny.