Introduction to Economics, EC 1001

Midterm Assignment
Introduction to Economics, EC 1001 Instructor: Dr. Sarvesh Bandhu
Spring 2021 Ashoka University
1. Consider a (small) linear city L of total length of 100Km (L = [0; 100]). It has no
restaurants so far and govt. has recently given permission to KFC to open its two
franchises, F1 and F2. Note that each franchise is owned by a di erent rm i.e. Fi
is operated by rm i, where i 2 N = f1; 2g). According to KFC norms, both rms
have to serve the same food item and charge the same price per unit of food, which
is decided by the head oce. Therefore, the only decision these rms need to make
is where to locate their restaurants. Assume that customers are uniformly located
over the entire city, which has a total mass of 100. Each customer needs to travel
to buy food and thus spends traveling cost in addition to the price of food. Because
price, quality and taste of food from each franchise is identical, a customer’s choice
of franchise primarily depends on the traveling cost and she prefers to buy from the
nearer franchise. And if a customer nds both the franchises at equal distance then
she divides her demand equally. Formally, for any two points x; y 2 [0; 100], d(x; y)
denotes the distance between them i.e. d(x; y) = jx 􀀀 yj. Suppose a customer stays at
point x and restaurants F1 and F2 are located at l1 and l2 respectively, then her choice
of restaurant is denoted by Cx(l1; l2) which is as follows:1
Cx(l1; l2) =
8>>< >>:
F1 if d(x; l1) < d(x; l2) F2 if d(x; l1) > d(x; l2)
fF1; F2g otherwise
Assume that each rm has equal constant per unit cost of production. As prices and
costs are xed2, maximizing the pro t is equivalent to maximizing the demand (which
is obviously based on locations of both rms).
This question has two parts, in each part preferences of customers and objectives of
rms remain the same.
(a) For a location choice (l1; l2), where l1  l2, compute the demand for each rm i.
1Note that each x; l1; l2 2 [0; 100]
2It is obvious that per unit price xed by the head oce is higher than per unit cost
1
(b) In this setup, we de ne a location choice (l?
1; l?
2) as an equilibrium, if no rm wants
to change its location, given the location choice of other rm i.e. given l?
2, rm
1 can not get higher pro ts by choosing some location other than l?
1. Similarly
given l?
1, rm 2 can not get higher pro ts by choosing some location other than l?
2.
Find such an equilibrium. Is it unique or could there be multiple such equilibria.
(c) Now assume that everything remains same but the only di erence is that now
there are three franchises, each operated by a di erent rm, franchise Fi operated
by rm i, where i 2 f1; 2; 3g. For this setup, we de ne an equilibrium in the
similar way. A location choice (l?
1; l?
2; l?
3) is an equilibrium, if no rm wants to
change its location given the location choice of other rms i.e. given l?
2 and l?
3,
rm 1 can not obtain higher pro ts by choosing some location other than l?
1. A
similar condition applies to rms 2 and 3. Find such an equilibrium.
2. The market demand and supply functions for an item are as follows:
qd = 24 􀀀 p
qs = 2p:
(a) Calculate the equilibrium price and quantity.
(b) Suppose the government imposes a per unit tax of Rs 1:50 on sellers. How is the
economic burden of the tax distributed across buyers and sellers? Also calculate
the deadweight loss of the tax.
(c) Consider a general tax rate t per unit, to be paid by the sellers. Find the value
of t that maximizes tax revenue for the government.
(d) If the government chooses t to maximize the sum of consumers’ surplus, producers’
surplus and tax revenue, what would be the optimum choice?
(e) Suppose a producers’ lobby can in
uence the government to set a price
oor p
that maximizes producers’ surplus rather than social surplus. What price
oor
will the lobby recommend? Calculate the deadweight loss, assuming sellers only
produce an amount equal to the quantity demanded at the controlled price.
(f) Suppose the government imposes a price ceiling p = 4, which is below the equilib-
rium price. However, the amount produced by rms at the ocial controlled price
2
is captured by unscrupulous middlemen, who sell it to consumers in an illegal but
competitive black market. Calculate the black market price, pro ts made by the
black marketeers and the social deadweight loss.
3. Suppose the inverse demand function is linear: p(q) = 􀀀 q. The monopolist’s cost
function is c(q) = q2. Assume the monopolist must charge a uniform price.
(a) Find the optimum monopoly price and quantity. Also calculate the deadweight
loss.
(b) Suppose the government can levy a lump-sum tax T (i.e., a xed amount indepen-
dent of production) and an excise tax t per unit of production on the monopolist.
These taxes can be negative, in which case they are subsidies. The proceeds of
these taxes can be transferred to consumers. The monopolist is always free to quit
the market, in which case she does not have to pay any taxes. The government
wants to maximize the consumer welfare. Find the optimum values of t and T.
4. The market for Chai is perfectly competitive. Each rm has a cost function given
by c(q) = 16 + q2, where q is the output produced by a rm. Any rm which stops
production has no cost. The inverse demand function is given by Q = 80 􀀀 p.
(a) Find and draw the supply curve of a competitive rm in this market.
(b) Suppose there are 8 price taking rms in the market. Find the equilibrium price
and quantity.3
(c) Now suppose there is free entry and exit in this market. New entrants will have
the same cost function. What is the equilibrium price, quantity and number of
rms in the long run?4
3A rm is willing to supply positive quantity only if it makes non-negative pro t.
4If rms are earning pro ts, then new rms will enter and if rms are making losses, then some rms exit
the market. In the long run, such changes would not occur.
3
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