# Microeconomic Theory

Total Marks: 25

1. An electrical utility company must produce electricity to meet the de-
mands of a city. The company is regulated by the city – it must charge

a fixed price specified by the government and it must meet all demand
at that price. The total demand for electricity over any 24 hour period
is known with certainty to be 13 units; however this demand differs
from day (6 AM to 6 PM) to night (6 PM to 6 AM). During the day
hours, 9 units of electricity are demanded, while during the night 4
units are demanded. This too is known with certainty.
The electric utility has the following production function for electricity:

qi = (KFi)
1/2

where i = d(day), n(night), K is the size of the generating plant, Fd is
the amount of fuel used in the plant during the day, Fn is the amount
of fuel used at night, qd is the amount of electricity produced during
the day, and qn is the amount of electricity produced at night. The firm
can vary its use of fuel from day to night, but it must build a single
generating plant – it cannot change the size of the plant from day to
night. Say a unit of plant costs r per 24 hour period and a unit of fuel
costs w.
(a) Conditional on the plant size K how much fuel will the company
use during the day (Fd) and night (Fn)? (5)
(b) What size of plant will the utility build? (10)
2. Answer True, False or Uncertain and provide an explanation. Dude’s

expenditure function is e(p, u). His demand function for White Rus-
sians (a cocktail consisting of vodka, Kahlua and cream) is xw(p, y),

1

where p is the vector of prices and y > 0 is his income. White Russians
are a normal good for Dude if and only if ∂
2
e(p, u)/∂pw∂u > 0, where

pw is the price of White Russians. (10)

2

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