3. What if instead the production function was given by:
$Q = min\{20L, 15K\}$
(a) Would we consider this technology to be relatively labor-intensive or capital-intensive? Explain.
(b) Does the production function display increasing, decreasing, or constant returns to scale? Please show with algebra by increasing inputs by a fixed factor $\theta$.
(c) Derive the equation of the isoquants corresponding to $Q = 16$, $Q = 9$, and $Q = 4$. Draw them on an isoquant map, placing $L$ on the horizontal axis and $K$ on the vertical axis. Label the axes and the output levels.
(d) Derive the equation of the Marginal Product of Labor ($MP_L$), assuming $K = \bar{K}$.
(e) Derive the equation of the Marginal Product of Capital ($MP_K$), assuming $L = \bar{L}$.
(f) Derive the equation of the Marginal Rate of Technical Substitution of Labor for Capital ($MRTS_{LK}$).
(g) If we need to fill an order for 100 ditches, what is the minimum amount of hours of labor you would hire? How would this number change if the production function were given by $Q = min\{50L, 50K\}$?