economy

Eco 361 Sum 17 Exam 1

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Vocab

Please define 5 of the following 7 vocab words. Along with the definition, please provide a hypothetical

example/scenario that applies said vocabulary concept. (4 pts each, 20 pts total)

1. Objective Function

2. Cross Price Elasticity of Demand

3. Isoquant

4. Indifference Curve

5. Law of Supply

6. Law of Diminishing Marginal Utility

7. Coefficient of Determination (𝑅2)

Eco 361 Sum 17 Exam 1

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Short Answer

Please answer 5 of the following 6 questions. (6 pts each, 30 pts total)

1. Income elasticity of demand is defined as:

𝐸𝑚 = %Δ𝑄𝑑 %Δ𝑚

*Where "𝑄𝑑 " represents quantity demanded and "𝑚" represents income.

If the good in question is normal, what should the sign of the coefficient be? Use the given equation

to explain. (6 pts)

2. Consider the following supply and demand curves:

𝑃𝑑 = 𝑎 − 𝑏𝑄

𝑃𝑠 = 𝑐 + 𝑑𝑄

*Where a,b,c, and d are all constants. Assume that 𝑎 > 𝑐.

Sketch a graph of this market and derive expressions for 𝑄∗ and 𝑃∗. Show all work. Briefly explain

why we are not interested in situations where 𝑎 < 𝑐. (6 pts)

3. Suppose a farmer wants to build a rectangular enclosure along an existing stone wall. If the side

along the wall needs no fence, find the dimensions of the largest enclosure that can be made with

500 feet of fence. Show all work.

4. Suppose you are a monopolist facing the following demand curve:

𝑃𝑑 = 𝑎 − 𝑏𝑄

Derive an expression for total revenue. Find its critical value. Is this a minimum or maximum? How

do you know? Explain/Show work. (6 pts)

5. Consider the following Cobb-Douglas production function:

𝑌 = 100𝐿√𝐾

Does this production function exhibit increasing, decreasing, or constant returns to scale? How do

you know? Explain. (6 pts)

Eco 361 Sum 17 Exam 1

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6. Consider the following Cobb – Douglas utility function:

𝑈 = 𝑋𝛼 𝑌𝛽

*Note, it should be assumed that 𝛼, 𝛽 > 0

Derive an expression for the marginal utility of good “X”. Show that the marginal utility of X is

downward sloping under diminishing and constant returns to scale. Does this negative slope always

hold when the utility function displays increasing returns to scale? Why / Why Not? (6 pts)

Eco 361 Sum 17 Exam 1

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Extended Response: Please answer all of the following questions. (50 pts possible)

1. Consider the following (Cobb-Douglas) utility function:

𝑈 = 𝑋1 𝛼 𝑋2

𝛽

And budget constraint:

𝑀 ≥ 𝑃1𝑋1 + 𝑃2𝑋2

*Treat 𝑃1, 𝑃2, 𝑀, 𝛼, and 𝛽 as positive constants.

Using these equations, please answer the following questions:

a. Formally state this consumer’s utility maximization problem and write down the relevant

Lagrangian. (5 pts)

b. Using your work from part “a.” , derive demand curves for 𝑋1 and 𝑋2. Show all work. (5 pts)

c. Show that the demand curves derived in part b. satisfy the rule of equal marginal utility per

dollar spent (i.e. 𝑀𝑈1

𝑃1 =

𝑀𝑈2

𝑃2 ). (5 pts)

d. Show that the law of demand holds for both 𝑋1 and 𝑋2. (5 pts)

e. Show that both 𝑋1 and 𝑋2 are normal. (5 pts)

f. Suppose 𝑀 = 1,000 and 𝛼 = 𝛽 = 1

2 . Using the midpoint method, please calculate the price

elasticity of demand for 𝑋1 when 𝑃1 changes from 1 to 5. Interpret the coefficient. How, if

at all, does this change in price influence the total revenue generated from this person’s

purchase of 𝑋1? Show all work/explain. (5 pts)

2. Consider the market for taxi rides in some hypothetical city. Explain, by using supply and demand

analysis, how each of the following actions will affect the market. Full credit answers should

identify/explain the relevant S/D shifter(s), incorporate supply and demand models into their

explanations, and carefully label their models. Please consider each case separately.

a. Bus drivers go on strike, causing bus fares to increase. (5 pts)

b. Gas prices increase. (5 pts)

c. The population of the city increases. (5 pts)

d. The population of the city decreases. (5 pts)

Eco 361 Sum 17 Exam 1

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Extra Credit Opportunity

1. Consider the following excerpt (from Ebay.com, Blog Stories):

In 1990, Nintendo held a 30- city gaming tournament to find the best player in the world. Players

had to get the best score in demo versions of three games – Super Mario Bros, Rad Racer, and Tetris

– all within a six minute time limit. At the end of each city’s tournament, the winners of each of the

three age groups were given special “championship cartridges” exactly like those used in the

competition. Ninety cartridges were distributed worldwide.

Meanwhile, Nintendo also released a special “gold edition” of this cartridge to those who won a

promotional contest in the pages of Nintendo Power magazine. Only 26 of these, gold edition,

cartridges were released.

a. According to this article the “championship cartridge” has a price range (at auction) of 10 -

20 thousand dollars (depending on condition). The last gold edition to sell on eBay went for

$26,677. Both types of cartridge contain the same set of games (played during the

tournament) and they likely costed essentially the same amount of money to produce (one

is simply painted gold and the other grey). Begging the question, why the difference in

price? Use supply and demand analysis to address this question. Explain. (5 pts)