Labor and Capital

Question 1

An economist thinks that wheat harvest increases over time as a result of technological development and estimates the following two equations for the yield of the wheat harvest (Ŷ_­t) as a function of time:

Ŷ_t = 0.50 + 0.010 t + 0.0030 t² (R² = 0.40)

Ŷ_t = 0.40 + 0.020 t + 0.15 ln t (R² = 0.60)

Answer the same questions for both estimated equations:

a) the estimated value of the wheat harvest if t = 45 and if t = 60

b) the estimated value of the slope dyt/dt if t = 45 and if t = 60

c) the estimated value of the elasticity (dyt/dt)*(t/yt) if t = 45

Question 2

Caluculate for both functions (a and b) the slope (dy/dx) as well as

the elasticity (dy/dx)* (x/y).

HINT: use the fact that d (lnxt) / d (xt) = 1 / xt = > d (lnxt) = d (xt) / xt

a) ln y_t = β₀ + β₁.(x_t)²

b) y_t = β₀ + β₁.(lnx_t)²

Question 3

See: A. H. Studenmund, Using Econometrics, Seventh Edition, Chapter 7, exercise 7, pages 233-234. (or Sixth edition, Chapter 7, exercise 7, page 238)

1. What are the elasticities of output with respect to labor and capital in each industry?
2. What economic significance does the sum (β₁ + β₂) have ?
3. Show that the elasticity of output (Q) with respect to labor and capital is respectively equal to β₁ and β₂ .