Econ 502
Applied Microeconomic
Theory
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Weekly Questions
(Updates likely, so check back)
These questions are intended to reinforce concepts and methods emphasized in the prior week's class.
Special Note: Because of Wix typesetting limitations, superscripts appear as ^( ). For example, x squared = x^(2)
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Week 1 Lecture Questions
Given the following information:
Utility = x^(1/2) * y^(1/2) ; Income = 200; price of x = 20 ; price of y = 10
(Note: You can convert utility function based on ln(x^a * y^b) = a*lnx - b*lny if you desire; also, exponents of 1/2 and 0.5 are the same)
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1. What is the consumer's MRS of y for x? What is the meaning of the MRS in terms of consumer choice?
2. Draw the budget constraint; what is the max amount of x possible? Max y? Slope of budget constraint?
3. Solve x and y for the level that maximizes consumer utility and calculate the utility at this point.
4. What happens to the budget constraint if the price of y increases to 20. What happens to the amount of x purchased when price of y increases to 20?
5. Derive an equation showing the change in the optimal amount of x for changes in the price of x. When the price of x changes, why does the optimal quantity of x change?
6. What is the role of theory? What problem arises with a solely "evidence-based" approach to answering questions?
7. Why might econ models that look like individual models actually be much better predictors of behavior at a group level?
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Week 2 Lecture Questions
1. Suppose that a consumer's income is $300 and that the price of x is $10 and the price of y is $10. Write out an equation for this budget constraint and a graphic to go with it. Then, the consumer is offered a lower price of $5 on each unit of x, but to
get the lower price, the consumer must join a club (Sam's, Costco, ...) for $100. Write out this constraint and add this line to your graphic.
2. Suppose that a state is concerned about the scarcity of water but also about access to it for low-income households. The state imposes a tax of (t) on water consumption but then gives a rebate of (r) to households where income falls below a threshold (I^T). Express the post-tax constraints for households above and below this threshold. Show a graphic that illustrates these different household constraints.
3. Suppose that a consumer generates income by earning wages and rental income that are both subject to taxation. The consumer also faces sales taxes on goods x and y. Express the income constraint for this consumer.
4. Suppose that a consumer is offered two phone plans both of which charge a fee for an amount of "free" minutes and then charge a price per minute above this threshold. Plan A charges twice the fee of Plan B, the minute threshold is twice as high on Plan A, and the fee for going over the threshold is twice as high on Plan B. Express these constraints as equations and in a graphic. Under what conditions would two households likely choose different plans? Under what conditions what two households likely choose Plan A even if their incomes are substantially different?
5. Rather than focusing on income, set up an equation that expresses the limits imposed by time and "expenditures" on two different activities.
6. In terms of driving behavior and outcomes, describe the effect of the addition of safety items to autos like airbags in terms of a "substitution effect" and an "income effect."
7. What is meant by "homothetic" preferences for Cobb-Douglas or CES Utility functions and how does the solution for the demand for x (x =Income/Px) relate to this idea. How does this relate to a topic like health care expenditures across countries?
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Week 3 Lecture Questions
1. How does Prescott's model of consumer choice
a) take into account the value of leisure?
b) take account of decisions over time and forward-looking nature of consumer choices?
c) take account risk and time preference?
2. In Prescott's budget constraint
a) What are the sources of income?
b) What are the expenditures?
c) What happens if the tax on labor is increased and what is the likely impact of this change on consumer choice?
3. a) Express a 2-period choice model where the consumer cares about consumption in two periods where utility in the two periods is logarithmic and additive with time preference of Beta^t. Income is generated by labor hours (L) at wage w, and there are no taxes on income or consumption. You should express the choice framework as a constrained optimization problem.
b) What are the choice variables for the household?
c) What are the "exogenous" variables and parameters that determine outcomes?
d) If the rate of time preference increases (meaning that present consumption is valued more highly), what would happen to present consumption?
4. a)What is something that you value that you produce with your own time and labor?
b) What market goods and services do you use to help produce this?
c) What kinds of things or changes in these things (attributes of household members, life events, market prices, ...) would influence the optimal decisions?
5. Explain the logic of Bill Belichick's decision to go for 4th and 2 on his own 28-yard line late in the 2009 game with the Colts. Why might a coach, who understands this logic, choose differently?
No Answers This Week; Questions are just review of class material
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Week 4 Lecture Questions
1. Use the Prisoner's Dilemma game presented in class to express the "Belling the Cat" case discussed in the "10 Tales of Strategy reading. Who are the participants in the game? Why do Dixit and Stiglitz view at as a version of the PD game?
2. In the "Here I Stand" tale from the "10 Tales," what aspect of strategic game tactics was DeGaulle skilled at using? How does this alter a game (either in normal form or extensive form)?
3. In a game setting known as the "Samaritan's Dilemma," there is a giver of aid and a recipient of aid. These might be two countries, a parent and adult (or nearly adult child), or other relationships. The giver has to decide whether to give aid or not and the recipient has to decide whether to engage in "good" or "bad" behavior (from the giver's perspective). The key to the payoff structure is that the giver's worst outcome is where the recipient is destitute (starving, ...) and the recipient knows this. Express this game in normal form.
4. Use extensive form framework to work out a solution to the "Battle of the Beach" problem (assume 2 taco trucks that can setup anywhere from point A to Z on a stretch of beach and there are no costs associated with moving to a new location; beachgoers are evenly distributed along the stretch of beach. What changes to this situation might lead to a different solution?)
5. Be able to identify the essentials characteristics of any game.
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Selected Answers (see bottom of the powerpoint slides)
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Week 5 Lecture Questions
Suppose that a firm has the following production, cost, and revenue functions:
Production: Q = 10*lnL
Cost: C = 25 + 10Q + Q^2
Revenue: R = P*Q
Demand (inverse): P = 100 - Q
1. What are marginal productivity and average productivity of labor? What is the marginal revenue product of labor? With L=10, what would MP of labor and AP of labor be? In a competitive market, with a price = 50, what would the MRP of labor be?
At what amount of Labor are the MP and AP of labor equal? What is the behavior of AP before and after this point?
2. What is the marginal cost and average cost? If Q=10, what are MC and AC? At what quantity are the MC and AC equal? What is the behavior of AC before and after this point (graph these equations). What would happen to this point if the 25 were changed to 1000? What does this imply about the role of fixed costs for the behavior of average costs and the relationship between AC and MC? (Make sure that you can set up a profit max problem in the case of choosing quantity of output and in the case where choosing quantity of inputs (labor and capital).
3. What is the marginal revenue? What is its relationship to the inverse demand equation? What does this imply about this firm and the market it is in?
4. Setup up the profit function so that it can be maximized based on choosing the optimal quantity. Set MR=MC and find the optimal quantity. Then, solve for the optimal price and optimal amount of labor. How would you need to set up the profit function differently if you wanted to maximize it based on (directly) choosing the optimal quantity of labor?
5. Express the Cobb-Douglas production function. How is related to the CES production function. What does "CES" stand for and what is the meaning of that? How is it related to the translog production function? (see ppt slide)
6. How does the meaning of "capital" in a production function differ at a firm level of analysis verses a macroeconomic level? What key economic principles are implied by production functions? (see the ppt slide)
7. Explain the logic behind using NFL player salaries to estimate an open-market value for college players. What adjustment to NFL salaries must be made? What economic issues might create errors in such estimates?
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Week 7 Lecture Questions
1. Express a general, algebraic formula for price elasticity. From an earlier problem, we solved for the demand for Qx = I/2Px. Find the slope of this demand equation (dQx/dPx), and then find the elasticity (it will be a formula). Using a supply & demand graphic, express why it is nearly impossible to estimate the price elasticity of demand using only if the only data available is on prices and quantities.
2. Write out demand and supply equations based on the most common economic influences but in a format that conforms to an empirical, regression framework. Explain the problem that arises in trying to use the results from a single equation estimate of these influences on quantity demanded to estimate the price elasticity of demand. How does the Fulton Fish market article solve this dilemma?
3. Explain the logic/methods used by Levitt et al in their Uber demand estimation study to distinguish movements up and down a demand curve (the price elasticity of demand) form shifts in the demand curve.
4. Many managerial economics textbooks state that if price and quantity data is available for a single firm, then a simple reduced-form equation can provide the price elasticity of demand. The same thing is often stated if "high frequency" data (such as daily or hourly). For this to be valid, what assumption must hold? Give an example of high-frequency data where this might work and might not work.
5. What economic fundamentals might explain the tendency for price increases and decreases to occur with different timing? What about the tendency for fuel prices to be more flexible than many other prices or "strategic prices" (sales or price discrimination) to be very flexible but "regular" (supply and demand) driven changes to be less flexible?
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Week 8 Lecture Questions
1. Express the graphic setup for the standard perfect competition model of market and firm pricing along with the monopoly/monopolistic competition model. What are the main differences between the two models in terms of predictions of prices and their relation to costs and profits?
2. In what ways are market conditions more complex than indicated by these models? How might these conditions make comparisons of price, costs, and profits based on the basic models misleading?
3. What was the focus of the Wollman AER article and how does it relate to the preceding question?
4. Using a simple pricing equation, express how one might try to assess whether two firms are "in the same market? What problems/limitations arise in trying to make such an assessment with data?
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Week 9 Lecture Questions
1. What transaction costs and the technologies behind them were critical to the emergence of services like Uber or Airbnb? What about the emergence of "big box" retailers like supermarkets?
2. Draw a graphic that depicts the situation where a firm faces a large fixed cost but a low and constant (or nearly constant) marginal cost of production. What does the average cost curve look like in this situation? If the price is set equal to marginal cost, what is the firm's profit? What is the firm's price if it sets MR=MC?
3. In the setting above, what is meant by "average cost pricing"? What problems for consumers arise when there is a regulatory policy of average cost pricing?
4. Describe why a few details of costs in electrical production that lead to its frequent use in illustrating #2. What about the cost structure in pharmaceutical firms? How might #2 figure into cable/satellite providers offering "a la carte" options only after a basic bundle is purchased? What is meant by "price discrimination" for offering higher tiers and what difficulties arise in distinguishing this from other forms of the large fixed cost pricing problem?
5. What are other mechanisms employed to deal with the large fixed cost problem? How might the structure of the problem in pharmaceutical drugs differ in the U.S. and a country like Canada?
6. How do geography impact demand, market shares, and pricing?
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Week 10 Lecture Questions
1. Setup the maximization model that reflects an asymmetric information setting where an owner relies on a manager's effort but cannot observe the manager's level of effort with precision. What is at the root of the problem for owners?
2. What are the steps to the owner trying to solve this problem as a sequential game? Express the participation constraint and the incentive compatibility constraint as a simple equation. Then, express the economic meaning of each.
3. What are other settings that are similar in their structure to the framework outlined in #1? What market mechanisms have developed to deal with it?
4. Setup the maximization problem that reflects an asymmetric information setting where the buyer (a profit maximizer) cannot observe a key attribute of sellers (consumers in the market).
5. Express the participation constraint and incentive compatibility constraint in this case both as a simple equation and in terms of their economic meaning.
6. Identify the fundamental economic influences on the optimality of rules versus discretion and match the following settings to the influence(s) that seem to matter a lot for each setting:
i) Good Samaritan Laws, ii) Military training, iii) Monetary policy, iv) Sully Miracle on the Hudson
7. What factors make it difficult to determine a set of conditions under future discretion is permitted or not, and why does this create problems of evaluation of performance/rewards-punishments?
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Week 11 Lecture Questions
1. Summarize two studies that give (somewhat) different evidence on the extent to which managers matter for productivity or other important outcomes of firms (not using sports). Why might these differences emerge in empirical studies?
2. Switching ports managers (head coaches and general managers) doesn't seem to matter systematically in sports very much. Why might sports provide different evidence from more general managerial contexts?
3. Resolve the paradox that while changing sports managers doesn't seem to matter much, including fixed effects for head coach or general managers improves explanatory power a lot. How might this relate to a statement that has been used in promoting the importance of "emotional intelligence" of managers that "IQ of CEOs doesn't matter for firm outcomes, but emotional intelligence does"?
4. What is meant by "management by design" v. "management as technology" in terms of economic frameworks? How would these be expressed differently in a simple algebraic framework?
5. Give an example of a managerial activity that would fit under "management by design" heading and an example that would fit under "management as technology" heading.
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Week 12 Lecture Questions
1. Draw a diagram that expresses the impact on sales and employment in Warren County of WKU. Clarify in this diagram what is meant by the "direct effect," "indirect effect", and "induced effect"?
2. What are the key determinations that an investigator must make in arriving at the economic impact estimate? Why might this be easier for an entity like WKU versus a prospective entity (like a new wagering facility like Kentucky Downs)?
3. How does a typical Cost-Benefit Analysis differ from a typical economic impact analysis?
4. Describe the key steps involved in estimates of the costs-benefits of the Seattle rail project
5. What are the key non-monetary benefits that require estimating in the rail project case and in the overpass case? How are they measured in these studies?
6. List a variety of methods that can be employed to place a monetary value on non-monetary costs or benefits such as the value of time, the value of life or injury, the value of pollution, ...
7. Outline the key measurements needed to generate a "back of the envelope" estimate of the life-extending or life-improving health care treatments. Be able to show with specific numbers why estimates into the trillions are quite reasonable.
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Week 7 Selected Answers
1. Elasticity of demand = %change Q/%change P
= (Q2 - Q1)/(P2 - P1) * (P1/Q1)
if Q* = I/2P
dQ*/dP = - I/(2P^2) and elasticity = - - I/(2P^2) *(P/Q) = - I/(2PQ)
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2, 3, and 5 should be in your notes
4. To use single-firm and/or high frequency data to estimate the elasticity of demand with a reduced-form approach implicitly assumes that the observed changes in prices are all due to the firm's strategic decisions and not by shifts in demand to which the firm might be responding. A case like UberX or prices for movie tickets at different times of day are cases where it is clear that the firm is responding to shifts in demand based on timing. It might be possible to account for this with day or time variables.
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