Microeconomics Assignment: Long-Run Supply and Tax Burden Analysis

This assignment solution delves into microeconomic principles, addressing questions on supply, demand, and taxation. The first part analyzes the long-run supply curve in a homogeneous market, examining how firms enter and exit based on profit. It includes calculations for optimal production levels and illustrates the long-run supply curve graphically. The second part investigates a market with a demand curve of Q=1/p and a supply curve of Q=p, initially in competitive equilibrium. It then examines the impact of a per-unit tax, calculating the tax burden distribution between consumers and producers and computing the deadweight loss. The solution provides detailed steps and mathematical derivations, including equations and graphical representations to illustrate the concepts.

Running head: MICROECONOMICS 1
Microeconomics
Student’s Name
Institution Affiliation
date

MICROECONOMICS 2
Q2
There is a fixed cost of 4 and the variable cost is q2 in this equation the level of optimal
production will be
p = MC= 2q⇒ q= p
2
the industry short run supply curve
Producers in the short-run produce at the optimal level, particularly q= p
2 . There are two things
that occur in the short run: The entry of firms is precluded where the maximum number of firms
is fixed at n and the fixed cost is compulsory making it inappropriate to make quality production
decisions.
Using the fact that all firms are homogenous, then
QSR=nq= nq
2 = ∀p ≥ 0
Thus, the industry short-run supply becomes a function beginning at the origin with a positive
gradient n
2 .
It is imperative to note that for global optimality, p ≥ AC =q is a condition that is always
satisfied.
Industry long-run supply curve
However, in the long-run all producers produce at the optimal level that is q= p
2 .Also each firm
will desire two enter the industry only if it gets positive profits (Munoz-Garcia, 2017). In
deducing the decision to venture in such a market, we look at the fixed cost as variable such that
p ≥ AC = ⇒ p ≥ 1
q +q ⇒ 2q ≥ 1
q +q
such that q ≥ 1 ⇒ p ≥ 2

MICROECONOMICS 3
thus, what it implies is that each firm will enter the market when the price is at p=2 and
producing precisely at q=1 unit. However, what if there are (n-1) firms already present in the
industry. Then
Qn−1
LR =(n-1) q =(n−1)q
2
Then the entry of the n-th firm at p=2 we will obtain Qn
LR=n. Then there will be a lower quantity
Qn −ϵ < Qn,thus some firms are compelled to leave allowing the remaining firms to enjoy non-
negative profits.
Since there are n − 1 ≥ 1, optimizing the firms to determine the price that each will produce is
slightly less than q= n
(n−1) and this results in a higher price such that the price becomes
Qn−1
LR =(n-1) q=(n−1) p
2 = n= Qn
LR
Thus p= 2n
n−1
Thus, the long run supply curve is a sawtooth. Where n-1 with the condition that n ≥2 are in the
market, then the long run supply curve would be Q= (n−1) p
2 with the price p=2 till the price
becomes p= 2n
n−1 and it is at this juncture that the price drops to p=2 following the entry of n-th
firms and production becomes Q= np
2

MICROECONOMICS 4
p Q(1) = p=2
4 Q(2) = p
3 Q(3) = 3p=2
8=3
p = 2
1 2 3 4 Q
Figure 3: Long Run Supply -Homogeneous case
2.A market has demand Q=1/p and supply curve Q=p. Initially, there’s no tax and the market is
at competitive equilibrium. Now suppose the government imposes a small per unit tax r.
(a) Compute the approximate share of tax burden on the demand side.
(b) Compute the approximate DWL
In equilibrium QS=Qd
Thus Qd= 1
P =P
P2=1
√ P2=√1
P =1 then Q=1
With tax of r
PC=Ps+t

MICROECONOMICS 5
Qd= 1
P +r=p
1-pr+ p2= p2-pr+1=0
With r being less than 1
p2-pr-1=0
dp
dr =2p-1=0
2p=1
P2=2
Dead weight loss= ½ *( p2− p1)*(Q2−Q1)
½*1*0=0

MICROECONOMICS 6
References
Munoz-Garcia, F. (2017). Advanced Microeconomic Theory. The MIT Press.
UVIC. (n.d.). Tax Basics. Retrieved from http://web.uvic.ca/~mfarnham/temp_pdfs/tax_basics
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