**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 t^{2} (R^{2} = 0.40)

Ŷ_{t} = 0.40 + 0.020 t + 0.15 ln t (R^{2} = 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} = β_{0} + β_{1}.(x_{t})^{2}

b) y_{t} = β_{0} + β_{1}.(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)

- What are the elasticities of output with respect to labor and capital in each industry?
- What economic significance does the sum (β
_{1}+ β_{2}) have ? - Show that the elasticity of output (Q) with respect to labor and capital is respectively equal to β
_{1}and β_{2}.