PROBLEM SET FOR CHAPTER 02: LECTURE 07
EXTERNALITIES
1. There are two plots of land: once for rice plantation (Plot A) and the other for
maize plantation (Plot B). If plot A is sprayed with pesticide, its annual yield will
increase according to the following function: Qrice = 10 – 2*Qpes. in which, Qrice is
additional output gained (measured by ton) if an additional unit of pesticide is
used. Qpes is number of pesticide units used. However, thank for adjacent
location to plot A, the likelihood to be damaged by pests in plot B has been
reduced. Thus, its yield has also increased by Qmaize = 5 – Qpes, in which Qmaize is
additional maize yield gained in plot B (measured by ton) if an additional
pesticide unit is sprayed in plot A. Price of rice is 5 RM per ton (RM is
hypothetical currency unit), while price of maize is 2 RM per ton and price of
pesticide is 6 RM per unit. Question:
(a) What is the efficient level of pesticide used by the landowner of plot A if he
concerns only his utility? How about if the utility of the landowner of plot B
is taken into account as well?
(b) In the former, what is deadweight loss of social welfare?
(c) What is the compensation amount that Plot B landowner should pay for Plot
A landowner to encourage him spraying more so that Plot B landowner can
enjoy the spillover effect of spraying?
2. MC for producing an additional ton of chemicals follows the function of MC =
100 + 5Q, while demand for such chemicals follow the function of Q = 60 - 1/3
P (in which, P and MC are measured as USD million per thousand tons, Q as
thousand tons). However, the chemical firm has used a common pond to
dispose its production waste. A fishery cooperative also uses the pond as its
fishing source. It is estimated that the waste disposed from production of an
additional ton of chemicals can reduce the fish catching volume by 4 tons. Fish
price is USD 10,000 per ton. The cooperative decides to sue the chemical firm
for the damage it suffers from chemical production.
(a) Before the sue, how much is optimal level of chemical production?
(b) If the court decides to limit chemical production at the socially optimum
level, how much will the chemical firm produce?
(c) What is deadweight loss of chemical production if the court does not
interfere?
(d) If the court decides that the firm has to compensate to the cooperative, what
is efficient level of compensation per ton of chemicals produced? In this case,
how much the chemical firm has to pay for the cooperative?