Cobb-Douglas production functionThis exercise discusses properties of the Cobb-Douglas production function and its use in the Solow model.
Suppose we have the following aggregateproductionfunctionY= F(K, L)=AKaL1-a,whereListhenumberofworkers,Kisthecapital stock,Aistechnology anda?(0,1)isthecapital shareofincome.
a) Calculate the marginal product of capital and of labor from the aggregateproductionfunction.
b) Show that the share of total income that is paid to workers is equal to 1- a,assuming that markets are competitive.
c) Derive output per workerfrom the aggregate productionfunction.