ECON 4310 — Study Notes & Practice Questions (Based on PS1) Summary & Study Notes

🧮 Problem 1 — Price Elasticity of Demand

Key idea: Use the arc elasticity formula to measure elasticity between two points on a linear demand curve. For demand $Q = 10000 - 10P$, calculate quantities at the two prices, then apply the arc formula.

Step-by-step approach:

• Compute $Q_1$ and $Q_2$: $Q_1 = 10000 - 10(500) = 5000$, $Q_2 = 10000 - 10(400) = 6000$.
• Arc elasticity formula: $E = \frac{(Q_2 - Q_1) / \left((Q_2 + Q_1)/2\right)}{(P_2 - P_1) / \left((P_2 + P_1)/2\right)}$.
• Plug values: $E = \frac{(6000 - 5000) / 5500}{(400 - 500) / 450} = \frac{1000/5500}{-100/450} \approx -0.818$.

Interpretation: The demand is inelastic in this price interval (|E| < 1). A 1% fall in price increases quantity demanded by about 0.82%.

🔁 Practice (similar style)

1. Suppose monthly demand is $Q = 8000 - 8P$. Compute the arc elasticity between $P = 600$ and $P = 400$ and interpret the result.
2. For $Q = 15000 - 15P$, compute arc elasticity between $P = 200$ and $P = 300$ and state whether demand is elastic or inelastic.

🧾 Sources

file:js75mskv146c4d2t98hdxt29g981qv7t — PS1 (3).pdf

📉 Problem 2 — Grossman Model & Recessions

Key idea: The Grossman health capital model treats health as a stock produced by time and market inputs. Recessions change wages, time allocation, and income; each channel affects health in different directions.

Why health might increase during the Great Recession:

• More leisure time: Job loss or reduced hours can increase time available for health-producing activities (sleep, exercise). With more time to invest in health, the stock of health can rise.
• Less work-related stress or hazardous work: Reduced exposure to stressful or dangerous jobs can improve health outcomes.

Why health might decrease during the Great Recession:

• Lower income reduces market inputs to health: Less ability to purchase medical care, nutritious food, or safer housing reduces health investments.
• Psychological stress and long-term effects: Unemployment and financial strain can raise stress and worsen health over time.

Graphical intuition (verbal): Draw a health production frontier/budget line with axes for time devoted to market work vs time for health investment. A fall in wage pivots the budget line (opportunity cost of time falls), changing optimal time allocation. A fall in income shifts the feasible set inward for market inputs.

🔁 Practice (similar style)

1. Using the Grossman model, draw and explain how an increase in mandatory overtime hours would likely affect health capital and health-related time allocation.
2. Consider a policy that provides a monthly stipend to unemployed workers. Explain two ways this policy could affect health in the Grossman framework.

🧾 Sources

file:js75mskv146c4d2t98hdxt29g981qv7t — PS1 (3).pdf

⏱ Problem 3 — Labor–Leisure & Health Time Allocation

Key idea: The labor–leisure budget constraint maps hours of market work (income) against leisure/time for non-market activities (including health investment). Changes in available time or health investment requirements shift or rotate the budget set.

Problem setup recap: Wage $w =$15/hour, needs 10 hours sleep; currently works 6 hours/day and spends 1 hour/day at the gym. If the gym closes, time spent on health falls and days lost to illness may increase.

Analysis insights:

• The original budget constraint: total available hours = 24; mandatory sleep leaves $24 - 10 = 14$ hours for work and leisure. With wage $w$, the slope of the budget line is $w$ (trade-off between leisure and consumption). Working 6 hours yields earnings $6w$.
• When gym closes: time available for work might increase, but health worsens so expected lost hours due to illness increase, effectively reducing available productive hours. This shifts/rotates the budget constraint inward (reduces effective labor time) and lowers attainable consumption-leisure bundles.
• Utility effect: With well-behaved (convex) indifference curves, losing the gym and facing more illness will generally lower overall utility because the feasible set shrinks and/or health deteriorates.

🔁 Practice (similar style)

1. A worker needs 8 hours sleep and has $w =$20/hour. They currently spend 2 hours/day on exercise. If exercise time is reduced and illness increases by 1 hour/day on average, show verbally how the budget set and optimal choice change.
2. Suppose an illness reduces productivity (wage effectively falls to $0.75w$ when sick). Discuss how this affects labor supply and leisure in the short run.

🧾 Sources

file:js75mskv146c4d2t98hdxt29g981qv7t — PS1 (3).pdf

🎲 Problem 4 — Lotteries, Expected Value & Risk Attitudes

Key idea: Calculate the expected value (EV) of the lottery and use the information to reason about risk preferences, being careful about what can and cannot be inferred.

Given lottery: roll a single die. Outcomes: roll 1 or 2 $\to$ win $90$ (probability $2/6 = 1/3$). Roll 3–6 $\to$ lose $42$ (probability $4/6 = 2/3$).

Compute EV:

• $EV = (1/3) \times 90 + (2/3) \times (-42) = 30 - 28 = 2$.
• So the lottery's expected monetary value is </span>2$.

Can we tell risk preference from indifference? Discussion:

• A risk-neutral person cares only about EV: they would accept any gamble with positive EV. If someone is indifferent between accepting the lottery and walking away (zero payoff), that suggests they are not strictly risk-neutral.
• Indifference to a lottery with positive EV is consistent with risk aversion (the person requires compensation beyond EV to accept risk). However, without knowing the individual's initial wealth or utility function, we cannot definitively classify them as risk averse, neutral, or loving based on one indifference alone.

🔁 Practice (similar style)

1. A lottery: with probability $1/4$ you win $200$, otherwise you lose $50$. Compute the EV and discuss whether indifference implies risk aversion.
2. Someone is indifferent between a sure $10$ and a lottery that pays $30$ with prob $0.4$ and $-5$ otherwise. Compute EV and explain what this implies (if anything) about risk attitude.

🧾 Sources

file:js75mskv146c4d2t98hdxt29g981qv7t — PS1 (3).pdf

✍️ Additional Practice (user request) — Extra Questions & Tips

Key idea: The user asked for practice questions similar to those in the provided problem set. Below are extra practice problems drawing on the same concepts: elasticity, Grossman model intuition, labor–leisure tradeoffs, and risk/lottery evaluation.

Extra practice questions (mixed):

1. Demand: $Q = 12000 - 12P$. Compute the arc elasticity between $P=250$ and $P=350$; interpret whether total revenue rises or falls when price decreases from $350$ to $250$.
2. Grossman: During a sudden rise in remote-work opportunities, explain two mechanisms that could improve health and two that could worsen health. Include how the budget constraint or time allocation changes.
3. Labor–Leisure: A worker has 16 discretionary hours after sleep. Wage $w =$18/hour. They currently work 8 hours and exercise 1 hour; a new policy mandates 2 hours of unpaid training per day for employed people. Explain graphically/verbal how this policy affects the budget constraint and labor supply choice.
4. Lottery: An agent faces the gamble: with prob $0.5$ earn $60$, with prob $0.5$ lose $30$. If the agent is indifferent between taking the gamble and receiving a sure $x$, find $x$ (in expected value terms) and discuss what the comparison reveals about risk attitude.

Study tips:

• Always write down the functional form (demand, utility, time constraint) first.
• For elasticity problems, compute quantities and apply the arc formula to avoid endpoint bias.
• For Grossman/labor–leisure questions, sketch the budget constraint and movement/tradeoffs; label axes (hours vs consumption) and show shifts/rotations.
• For risk questions, compute EV and remember that indifference to a positive EV typically signals risk aversion, but classification requires more information.

🧾 Sources

text:user-input — Text Input