The economy of Wonderland produces magic potions using capital (K) and labor (L). Total output is growing at the rate of 5% per year. The rental rate per unit of capital is 0.1 bottles of magic potion. The physical capital-output ratio is 3:1. The stocks of capital and population are growing at the rate of 3 and 2% respectively. Assume that everybody works.

(a) If all output is paid in wages and rent, calculate the shares of capital and labor in national income.

(b) Estimate the rate of technical progress (or TFP growth) in Wonderland.

(c) Suppose that doubling the inputs results in 2.5 times the original quantity of magic potion. How does this affect your answer to part (b)?

(d) Suppose the owners of capital possess patent rights over their inventions and the rental rate reflects the monopoly price on capital rentals. How does this affect the growth-accounting approach used in the foregoing answers?

(e) Suppose that only half the labor population is engaged in production at any date. How does this affect your answer? If this proportion is increasing over time, what would happen to your estimate?