perfect competition - queen's...

Perfect CompetitionECON 212 Lecture 13

Tianyi Wang

Queen’s Univeristy

Winter 2013

Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 13 Winter 2013 1 / 12

Intro

I We can analyze firm’s supply decision.I Firm faces two constraints: technology and market.I Market constraint is summarized by the demand curve.I Demand curve facing the firm differs from market demand curve.

I one firm, two firms, ...I see graphs later.

I We start with the simplest market enviroment: perfect competition.


Perfect Competittion

I Market is perfectly competititve if there are large number of firms sothat each one is too small to influence market price.

I Firm’s problem: how much to produce taken price as given.I Strong assumption, works well.I See class notes for graph of Deman facing a Competitive firm.


Supply Decision of a Competitive Firm

I Here we take the cost sturcture as given.

I Competitve firm’s problem is

maxqpq − c(q)

I Note we can backup input demands after solving for q.I FOC is

p − c ′(q) = 0I or

p = MC (q)

MR(q) = MC (q)

I Competitive firm’s supply curve is its MC curve.I However there are two issues.





maxqpq − c(q)

I Note we can backup input demands after solving for q.

I FOC isp − c ′(q) = 0

I or

p = MC (q)

MR(q) = MC (q)






maxqpq − c(q)


p − c ′(q) = 0

I or

p = MC (q)

MR(q) = MC (q)






maxqpq − c(q)


p − c ′(q) = 0I or

p = MC (q)

MR(q) = MC (q)






maxqpq − c(q)


p − c ′(q) = 0I or

p = MC (q)

MR(q) = MC (q)

I Competitive firm’s supply curve is its MC curve.

I However there are two issues.





maxqpq − c(q)


p − c ′(q) = 0I or

p = MC (q)

MR(q) = MC (q)



Competitive Firm’s Supply Curve

I We derived supply curve from FOC. It could either be a max or a min.I See class notes graph where two output levels satisfy FOC.I Note we can avoid q1 by checking SOC.I Graphically this happens on declining portion of MC.I So firm’s supply curve is only the upward sloping portion of MC.


Competitive Firm’s Supply Curve (Con’t)

I Second issue is if price is so low that not profitable to produce.I See class notes for shutdown condtion.I Note: shutdown is different from exit.I So only upward sloping portion of MC above AVC is competitvefirm’s supply curve.


Long-run Supply of Competitive Firm

I Long-run curve intersects shrot-run curve at output q∗ where fixedfactor is optimal.

I See class notes for graph.

I LR curve is more responsive to price.I Firm can exit in the long-run. Thus profit has to be greater than zero.

pq − c(q) ≥ 0

p ≥ c(q)q

I Thus long-run supply curve is the upward sloping portion of LRMCabove LRAC.

I See class notes for constant returns to scale technology.




I See class notes for graph.I LR curve is more responsive to price.

I Firm can exit in the long-run. Thus profit has to be greater than zero.

pq − c(q) ≥ 0

p ≥ c(q)q






I See class notes for graph.I LR curve is more responsive to price.I Firm can exit in the long-run. Thus profit has to be greater than zero.

pq − c(q) ≥ 0

p ≥ c(q)q




Short-run Industry Supply

I Suppose there are n firms, let Si (p) be firm i’s supply curve. Thenthe industry/market supply is

S(p) =n

∑i=1Si (p)

I If firms are identical, S(p) = nSi (p)I Market demand and market supply determines equilibrium price andoutput level.


Long-run Industry Equilibrium

I If no barriers to entry, firms enter and exit in the long-run.I Firms entry and exit affect output produced and therefore equilibriumprice.

I We can get market supply by adding up individuals.I Will get an approximation. See class notes.I Note LR industry supply looks the same as firm supply with CRStechnology.


Long-run Industry Equilibrium

I In Competitive Equilibrium, we have Demand = Supply and each firmmax profit.

1. Firm max profit: p∗ = LMC (q∗)2. Perfect competition: p∗ = LAC (q∗)3. Market clears: QD (p∗) = QS (p∗) = n∗q∗


Opportunity Cost and Economic Rent

I Suppost entry is limited in some industries (Agriculture) due tolimited fixed factors (Land).

I It might look like farmer earns positive profit π.

I This not correct, we do not measure opportunity cost of Land.I Farmer can sell the Land for π.

I Whenever a fixed factor is preventing entry, a rental rate for thatfactor exists.

I This is Economic Rent: payments to a factor of production in excessof the minimum necessary to have that factor supplied.





I This not correct, we do not measure opportunity cost of Land.

I Farmer can sell the Land for π.







I This not correct, we do not measure opportunity cost of Land.I Farmer can sell the Land for π.




(Optional) Relationship b/w Cost-Min and Profit-Max

I Directly write profit max problem:

maxqpq − (wL+ rK )

s.t. q = Q(L,K )

I How to solve? sub constraint into objective by eliminating q.

maxK ,L

pQ(L,K )− (wL+ rK )

I FOC for K and L respectively are

pQ ′k = r

pQ ′L = w

I Take the ratio, we get the optimality cond’t for cost-min.

MPKMPL

=rw


perfect competition - queen's...

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