ECON 310-1
MIDTERM 2 — MASTER STUDY GUIDE
Northwestern University · Spring 2026
Production · Costs · Perfect Competition · Long-Run Equilibrium
HOW TO USE THIS GUIDE
Coverage: Every concept from your lecture notes, PS4, PS5, Practice Exam I, and Practice
Exam II. Nothing omitted.
Structure: Each topic follows the same pattern: Self-Quiz → Concept Explained Deeply →
Formulas → Worked Problems → Exam Techniques → Common Traps.
How to study: Try the Self-Quiz cold before reading the section. The quiz + trap sections
are specifically built to catch the mistakes that show up most on this exam.
The #1 priority topics: Lagrangian cost minimization, SR/LR cost derivation, profit
maximization (unit argument + SOSC), and the shutdown rule — these appear in virtually
every problem set and practice exam question.
, SECTION 1
Production Theory — The Foundation of Everything
SELF-QUIZ — Test Yourself Before Reading On
Q1: What does the production function Q = F(K,L) tell us? What assumption does the
professor make about F?
Answer: It gives the MAXIMUM output achievable from given inputs K and L. F is assumed
deterministic — once inputs are known, output is exactly known.
Q2: What is an isoquant? Why can't you apply the Monotonic Transformation Theorem to
isoquants?
Answer: An isoquant shows all (K,L) combinations producing a given Q. Unlike indifference curves,
isoquant values are CARDINAL (they measure actual output), so you cannot rescale them arbitrarily.
Q3: If MPL = 12 and MPK = 6, and w = 3, r = 6, is the firm minimizing cost? If not, what
should it do?
Answer: MPL/w = 12/3 = 4. MPK/r = 6/6 = 1. Since 4 > 1, NOT minimizing. Should use more L and
less K.
1.1 — The Production Function
DEFINITION: Production Function
Q = F(K, L), where Q = output, K = capital (machines, buildings, equipment), L = labor
(workers). The function gives the MAXIMUM output obtainable from any input combination.
Key assumption: F is deterministic — the firm controls inputs, and inputs determine output
exactly.
Sunk Costs: Costs already paid that cannot be recovered. They are IRRELEVANT to all future
decisions. The movie example: you paid for boring tickets. The cost is sunk — leave or stay based only
on whether you enjoy the next 90 minutes, not what you paid.
1.2 — Isoquants
DEFINITION: Isoquant
A curve showing ALL combinations of K and L that produce the same level of output Q. It is
the firm's analogue of the consumer's indifference curve — but with one critical difference:
the output numbers ON isoquants are meaningful (cardinal), not just rankings (ordinal). An
isoquant labeled Q=100 produces exactly twice what Q=50 produces.
The 4 Properties of Isoquants (you may need to prove these — see Practice Exam II Q22):
, Prope
Statement Why It Holds
rty
1. If L increases, K must Both inputs are productive — can't add one without
Down decrease to hold Q constant removing the other to stay on same isoquant
ward
slopin
g
2. Isoquants farther from origin Both inputs productive: more of both → more output
Higher represent higher Q
= more
output
3. Two isoquants never cross Transitivity: one input combo can't simultaneously produce
Canno two different output levels
t
interse
ct
4. Bow-shaped toward origin Inputs substitute for each other, but imperfectly — MRTS
Conve diminishes as you move down the isoquant
x to
origin
⚠ COMMON MISTAKE — Isoquants vs. Indifference Curves
You CANNOT apply the Monotonic Transformation Theorem to isoquants. With ICs, only the
ranking matters — any increasing transformation preserves preferences. With isoquants,
the NUMBERS matter. F(K,L) = 100 means exactly 100 units. You cannot replace it with 2F
or log(F) without changing the production technology. This comes up in MC questions about
isoquant properties.
The MRTS — Marginal Rate of Technical Substitution
FORMULAS — MRTS
Definition (geometric):
MRTS = |dK/dL| = |slope of isoquant|
How much K can be reduced per unit increase in L while keeping Q constant.
Formula (from production):
MRTS = MPL / MPK
Derive by taking the total differential of F(K,L) = Q along the isoquant (dQ=0).
Derivation:
dQ = MPK·dK + MPL·dL = 0 → dK/dL = -MPL/MPK → MRTS = MPL/MPK
, Diminishing MRTS: As you move DOWN and RIGHT along an isoquant (more L, less K), the MRTS
decreases. This makes isoquants convex to the origin. Economically: as you hire more workers and
remove machines, each additional worker substitutes for fewer and fewer machines.
EXAM TECHNIQUE — Checking for Diminishing MRTS
Method: Compute MRTS = MPL/MPK. Check if MRTS decreases as L increases (holding Q
constant along the isoquant).
PS4 Q7: Q = LK^(1/2)
MPL = dQ/dL = K^(1/2). MPK = dQ/dK = L/(2K^(1/2)).
MRTS = K^(1/2) / [L/(2K^(1/2))] = 2K/L.
As L increases along the isoquant, K decreases, so MRTS = 2K/L falls. YES, diminishing
MRTS.
PS4 Q8: Q = AL + BK (perfect substitutes)
MPL = A. MPK = B. MRTS = A/B = CONSTANT.
MRTS does not diminish — isoquants are straight lines (perfect substitutes). NO diminishing
MRTS.
1.3 — Short Run vs. Long Run
Short Run (SR) Long Run (LR)
Definition ≥1 input is FIXED — firm cannot adjust ALL inputs are variable — firm can
it choose any combination
Capital K Fixed at K̄ (given) Variable — firm chooses K
Labor L Variable — firm chooses L Variable — firm chooses L
Isoquant map Not applicable — K is fixed, so you Full isoquant map applies
move only horizontally
Real-world time Bike messenger ~2 days; Nuclear plant Depends on industry
~5-7 years
1.4 — Short-Run Production: TPL, MPL, APL
DEFINITION: Total Product of Labor (TPL)
TPL = Q = F(K̄, L). With capital fixed, output depends only on labor. The typical TPL curve:
rises slowly at first, accelerates through an inflection point (where MPL is maximized), then
flattens and eventually turns down (where MPL = 0, then MPL < 0).
FORMULAS — MPL and APL
MIDTERM 2 — MASTER STUDY GUIDE
Northwestern University · Spring 2026
Production · Costs · Perfect Competition · Long-Run Equilibrium
HOW TO USE THIS GUIDE
Coverage: Every concept from your lecture notes, PS4, PS5, Practice Exam I, and Practice
Exam II. Nothing omitted.
Structure: Each topic follows the same pattern: Self-Quiz → Concept Explained Deeply →
Formulas → Worked Problems → Exam Techniques → Common Traps.
How to study: Try the Self-Quiz cold before reading the section. The quiz + trap sections
are specifically built to catch the mistakes that show up most on this exam.
The #1 priority topics: Lagrangian cost minimization, SR/LR cost derivation, profit
maximization (unit argument + SOSC), and the shutdown rule — these appear in virtually
every problem set and practice exam question.
, SECTION 1
Production Theory — The Foundation of Everything
SELF-QUIZ — Test Yourself Before Reading On
Q1: What does the production function Q = F(K,L) tell us? What assumption does the
professor make about F?
Answer: It gives the MAXIMUM output achievable from given inputs K and L. F is assumed
deterministic — once inputs are known, output is exactly known.
Q2: What is an isoquant? Why can't you apply the Monotonic Transformation Theorem to
isoquants?
Answer: An isoquant shows all (K,L) combinations producing a given Q. Unlike indifference curves,
isoquant values are CARDINAL (they measure actual output), so you cannot rescale them arbitrarily.
Q3: If MPL = 12 and MPK = 6, and w = 3, r = 6, is the firm minimizing cost? If not, what
should it do?
Answer: MPL/w = 12/3 = 4. MPK/r = 6/6 = 1. Since 4 > 1, NOT minimizing. Should use more L and
less K.
1.1 — The Production Function
DEFINITION: Production Function
Q = F(K, L), where Q = output, K = capital (machines, buildings, equipment), L = labor
(workers). The function gives the MAXIMUM output obtainable from any input combination.
Key assumption: F is deterministic — the firm controls inputs, and inputs determine output
exactly.
Sunk Costs: Costs already paid that cannot be recovered. They are IRRELEVANT to all future
decisions. The movie example: you paid for boring tickets. The cost is sunk — leave or stay based only
on whether you enjoy the next 90 minutes, not what you paid.
1.2 — Isoquants
DEFINITION: Isoquant
A curve showing ALL combinations of K and L that produce the same level of output Q. It is
the firm's analogue of the consumer's indifference curve — but with one critical difference:
the output numbers ON isoquants are meaningful (cardinal), not just rankings (ordinal). An
isoquant labeled Q=100 produces exactly twice what Q=50 produces.
The 4 Properties of Isoquants (you may need to prove these — see Practice Exam II Q22):
, Prope
Statement Why It Holds
rty
1. If L increases, K must Both inputs are productive — can't add one without
Down decrease to hold Q constant removing the other to stay on same isoquant
ward
slopin
g
2. Isoquants farther from origin Both inputs productive: more of both → more output
Higher represent higher Q
= more
output
3. Two isoquants never cross Transitivity: one input combo can't simultaneously produce
Canno two different output levels
t
interse
ct
4. Bow-shaped toward origin Inputs substitute for each other, but imperfectly — MRTS
Conve diminishes as you move down the isoquant
x to
origin
⚠ COMMON MISTAKE — Isoquants vs. Indifference Curves
You CANNOT apply the Monotonic Transformation Theorem to isoquants. With ICs, only the
ranking matters — any increasing transformation preserves preferences. With isoquants,
the NUMBERS matter. F(K,L) = 100 means exactly 100 units. You cannot replace it with 2F
or log(F) without changing the production technology. This comes up in MC questions about
isoquant properties.
The MRTS — Marginal Rate of Technical Substitution
FORMULAS — MRTS
Definition (geometric):
MRTS = |dK/dL| = |slope of isoquant|
How much K can be reduced per unit increase in L while keeping Q constant.
Formula (from production):
MRTS = MPL / MPK
Derive by taking the total differential of F(K,L) = Q along the isoquant (dQ=0).
Derivation:
dQ = MPK·dK + MPL·dL = 0 → dK/dL = -MPL/MPK → MRTS = MPL/MPK
, Diminishing MRTS: As you move DOWN and RIGHT along an isoquant (more L, less K), the MRTS
decreases. This makes isoquants convex to the origin. Economically: as you hire more workers and
remove machines, each additional worker substitutes for fewer and fewer machines.
EXAM TECHNIQUE — Checking for Diminishing MRTS
Method: Compute MRTS = MPL/MPK. Check if MRTS decreases as L increases (holding Q
constant along the isoquant).
PS4 Q7: Q = LK^(1/2)
MPL = dQ/dL = K^(1/2). MPK = dQ/dK = L/(2K^(1/2)).
MRTS = K^(1/2) / [L/(2K^(1/2))] = 2K/L.
As L increases along the isoquant, K decreases, so MRTS = 2K/L falls. YES, diminishing
MRTS.
PS4 Q8: Q = AL + BK (perfect substitutes)
MPL = A. MPK = B. MRTS = A/B = CONSTANT.
MRTS does not diminish — isoquants are straight lines (perfect substitutes). NO diminishing
MRTS.
1.3 — Short Run vs. Long Run
Short Run (SR) Long Run (LR)
Definition ≥1 input is FIXED — firm cannot adjust ALL inputs are variable — firm can
it choose any combination
Capital K Fixed at K̄ (given) Variable — firm chooses K
Labor L Variable — firm chooses L Variable — firm chooses L
Isoquant map Not applicable — K is fixed, so you Full isoquant map applies
move only horizontally
Real-world time Bike messenger ~2 days; Nuclear plant Depends on industry
~5-7 years
1.4 — Short-Run Production: TPL, MPL, APL
DEFINITION: Total Product of Labor (TPL)
TPL = Q = F(K̄, L). With capital fixed, output depends only on labor. The typical TPL curve:
rises slowly at first, accelerates through an inflection point (where MPL is maximized), then
flattens and eventually turns down (where MPL = 0, then MPL < 0).
FORMULAS — MPL and APL
