A closed economy has the following production function:

Y=3K^1/3L^2/3

where Y denotes output, K denotes capital, and L denotes labor.

(a) If both capital and labor increase by 30%, what would be the percentage change in output?

(b) Assume that CAPITAL increases but labor stays constant

(i) Will the marginal product of CAPITAL increase, decrease, or stay the same?

(ii) Will the marginal product of LABOR increase, decrease, or stay the same?

(c) Assume that LABOR increases but capital stays constant

(i) Will the marginal product of LABOR increase, decrease, or stay the same?

(ii) Will the marginal product of CAPITAL increase, decrease, or stay the same?

(d) Assume that markets are competitive and national income is $21 trillion.

(i) Find total capital income (the total income of the owners of capital).

(ii) Find total labor income (the total income of all the workers).