ECON 6912: Microeconomic Theory
Study Guide for Midterm 2
Major Topics:
1. Choice Under Uncertainty
a. Expected Value vs. Expected Utility
i. Determining Risk Behavior
1. Risk averse, loving, neutral
b. Insurance
i. Reservation price
Kahneman and Tversky
a. Differences with classical model
b. Interesting insights
c. What the model says about risk behavior
2. Production
a. Marginal and average productivity
i. Diminishing Returns and Thomas Malthus
b. Isoquants
i. Marginal rate of technical substitution
c. Returns to scale
d. The 4 Production Functions (perfect subs, fixed proportions, Dobb-Douglas, and
CES)
i. Elasticity of substitution
e. Improvements in Technical Productivity (and technological unemployment)
3. Costs
a.
b.
c.
d.
e.
f.
g.
4.
Marginal and Average Costs (formulas and graphs)
i. Relationship with productivity.
Fixed and variable costs
Solving for cost as a function of output.
Relationship between marginal costs and marginal productivity
How to find cost minimizing allocation of inputs
i. How it depends on input prices and differences between nations
Relationship between costs and returns to scale
Long-run and short-run costs relationship
i. How to derive long run total cost functions (function of Q, w, r)
ii. Solving for contingent demand functions for L and K
Profit Maximization
a. Profit maximizing condition
b. Relationship between TR/TC curves, and MR/MC curves and profit curve
c. Marginal Revenue
i. Relationship with demand and with elasticity
d. Ability to charge price above MC
e. How to find profit maximizing price and quantity
f. Profit Function
i. How profits change when prices of product or inputs change
ii. First derivatives of profit function
1
Practice Problems
Note: The test will consist of approximately 12 short answer questions. The practice problems
below are just a sample of some of the types of questions you’ll be asked on the exam. You
should also study your assignment and your notes from class. Enjoy the questions!
1. You are a contestant on the famous game show "Let's Make a Deal" and Monty Hall has
selected you as a final contestant. You have a choice: you can take $64 in cash or you can
gamble. If you decide to gamble, there are three possible outcomes: door number one, door
number two, and door number three. Behind one of the doors is a prize valued at $100, another
door has a prize valued at $81, and one door has a prize worth $1.
a. What is the expected value of the gamble?
b. If you are risk neutral, which option would you choose?
c. Suppose your utility function is of the form u = M1/2; which option would you choose?
d. Suppose your utility function is of the form u = M1/2; what is the smallest amount of money
that Monty could offer you (with certainty) so that you would just be indifferent between the sure
thing and the gamble?
2. Ms Fogg is planning an around-the-world trip on which she plans to spend $10,000. The
utility from the trip is a function of how much she actually spends on it (Y), given by U(Y) = ln Y
a. If there is a 25 percent probability that Ms. Fogg will lose $1000 of her cash on the trip, what
is the trip’s expected utility?
b. Suppose the Ms. Fogg can buy insurance against losing the $1000 (say by purchasing
traveler’s checks) at an “actuarially fair” premium of $250. Show that her expected utility is
higher is she purchases this insurance than if she faces the chance of losing the $1000 without
insurance.
c. What is the maximum amount that Ms. Fogg would be willing to pay to insure her $1000?
d. If you did part B. correctly you found that Ms Fogg was willing to buy insurance against a 25
percent change of losing $1000 of her cash on her around-the-world trip. Suppose that people
who buy such insurance tend to become more careless with their cash and that their probability of
losing $1000 rises to 30%. What is the actuarially fair insurance premium in this situation? What
economic concept does this situation relate to? Will Ms. Fogg buy insurance now?
3. A farmer’s tomato crop is wilting, and he must decide whether or not to water it. If he waters
the tomatoes, or if it rains, the crop will yield $1000 in profits, but if the tomatoes do not get any
water, the crop will yield only $500. Operation of the farmer’s irrigation system costs $100. The
farmer is risk neutral and he seeks to maximize expected profits from tomato sales.
a) If the farmer believes that there is a 50 percent chance of rain, will he water the tomatoes?
b) What is the maximum amount the farmer would pay to obtain information from an itinerant
weather forecaster who can predict rain with 100 percent accuracy?
c) How would your answer to part (b) change if the farmer were risk averse?
2
4. According to the Kahneman-Tversky (hedonic framing model), which of the following
options would most people prefer to the other?
a.) Option 1: A gain of $5,000 or Option 2: a gain of $6,000 and a loss of $1,000?
b.) Option 1: A loss of $5,000 or Option 2: a loss of $4,000 and a loss of $1,000?
c.) Option 1: A 50% chance of losing $1,000 and a 50% chance of losing $0 or
Option 2: A sure loss of $480?
5. A firm has the following production function Q=2K1/3 L1/3
a. What is the marginal product of labor if K is fixed at 27?
b. Show whether the firm experiencing increasing, decreasing, or constant returns to scale.
c. Calculate the total cost as a function of Q.
d. What is the marginal cost if w=$10 and L=50?
e. What is the profit maximizing amount of K and L if r=$50, w=$100 and the firm cannot spend
more than $2,000?
6. When a firm is experiencing increasing returns to scale, what is happening to the long run total
cost function and what is happening to the long run average cost function?
7. When the average product of labor equals the marginal product of labor, how will marginal
cost compare with average variable cost?
8. A firm has access to two production processes with the following marginal cost curves:
MC1=0.8Q and MC2=10+0.6Q.
If the firm needs to produce 40 units of output, how much should it produce with each process?
9. Professor Smith and Professor Jones are going to produce a new introductory textbook. As
true economists, they have laid out the production function for the book as
Q= S0. 5 J0. 5
Where q equals the number of pages in the finished book, S equals the number of working hours
spent by Smith, and J equals the number of hours spent working by Jones.
Smith values his labor as $3 per working hour. He has spent 900 hours preparing the first draft.
Jones, whose labor is valued at $12 per working hour, will revise Smith’s draft to complete the
book.
a. How many hours will Jones have to spend to produce a finished book of 150 pages? Of 300
pages? Of 450 pages?
b. What is the marginal cost of the 150th page of the finished book? Of the 300th page? Of the
450th page?
3
10. Doug wants to go into the donut business. For $500 per month he can rent a bakery complete
with all the equipment he needs to make a dozen different kinds of donuts (K=l). He must pay
unionized donut bakers a monthly salary of $400 each. He projects his production function to be
Q = 5KL (where Q is tons of donuts/month).
a. What is Doug's monthly total cost function, variable cost function, and marginal cost?
b. How many bakers will Doug hire to make 25 tons of donuts?
c. What will happen to Doug's total cost if his production function turns out to be Q=2KL?
11. (16) An entrepreneur purchases two firms that produce the same good. Each firm has a
production function given by:
q  K i L i where i=1,2, referring to the amount of the input employed by either firm.
The firms differ in the amount of capital equipment they have. Firm 1 has K1 =25 and firm 2 has
K 2 =100. For simplicity, the prices of K and L are normalized to $1 for each.
a. If the entrepreneur wishes to minimize short run total costs of production, how much should be
produced in each firm (find Q in firm 1 as a function of firm 2 or vice versa).
b. How much should be produced by each firm if the entrepreneur wishes to produce 100 units?
c. Given that output is optimally allocated, calculate the short-run total, average, and marginal
cost curves as a function of quantity produced.
d. What is the marginal cost of the 100th unit? The 200th unit?
12. Given the following production function:
Q = 4L.8 K.8
a. Show the function has a diminishing rate of technical substitution.
b. Assume the wage rate (w) is 25 and the rental rate of capital (v) is 100. Solve for the cost
minimizing levels of L and K to produce 1296 units of output. What is the total cost of producing
in the long run?
c. Assume in the short run that the level of capital is fixed at 10 units. What would be
the short run total cost of producing 1296 units of output? Compare the long run cost of
producing 1296 units of output to the short run cost of producing 1296 units of output
(which is greater and why?)
13. Suppose the long-run total cost function for a firm is given by:
LRTC = Qw2/3 v1/3
a. Calculate TC at Q = 100 and Q =150 if w = $15 and r = $27. Is this firm experiencing
increasing, decreasing, or constant returns to scale? Explain.
b. Use the cost function to calculate the contingent demand functions for K and L.
4
14. Assume a single price firm is charging a price of $40, and is operating on a portion of the
demand where the elasticity equals -2. What is the marginal revenue? What is the marginal cost?
15. A perfectly competitive firm has a total cost function given by: 0.1q2 + 10q + 500 and the
market price is constant at P=$30 for all quantities produced.
a. What is the profit maximizing quantity of production for this firm?
b. What is their maximum attainable profit?
c. Will this firm shutdown or continue to produce? How do you know?
5