9 Some economists believe that the Australian economy as a whole can be modelled with the following production function, called the Cobb-Douglas production function:

y = A!(ll3 L 2/3 where Y is the amount of output, K is the amount of capital, Lis the amount of labour and A is a parameter that measures the state of technology. For this production function, the marginal product of labour is MPL = 213 A(KIL)113 Suppose that the price of output Pis 2, A is 3, K is 1 000 000 and L is 1000. The labour market is competitive, so labour is paid the value of its marginal product.

a Calculate the amount of output produced Y and the dollar value of output PY.

b Calculate the wage Wand the real wage WIP. (Note: The wage is labour compensation measured in dollars, whereas the real wage is labour compensation measured in units of output.)

c Calculate the labour share (the fraction of the value of output that is paid to labour), which is (WL)/(PY).

d Calculate what happens to output Y, the wage W, the real wage WIP, and the labour share (WL)l(PY) in each of the following scenarios:

Inflation increases P from 2 to 3.

ii Technological progress increases A from 3 to 9.

iii Capital accumulation increases Kfrom 1 000 000 to 8 000 000.

iv A plague decreases L from 1000 to 125.

e Despite many changes in the Australian economy over time, the labour share has been relatively stable. Is this observation consistent with the Cobb-Douglas production function? Explain.