Microeconomics, Module 4, “Consumers in the Marketplace”

Homework Assignment

(The attached PDF file has better formatting.)

The first four homework problems review elasticities; show the formula (or the solution method) and the solution.

Exercise 4.1: Price Elasticity of Demand

The price of a good is $200, and the quantity demanded is 2,000. The price elasticity of demand is –1.25. If the price changes to $204, what is the new quantity demanded?

Exercise 4.2: Income Elasticity of Demand

A consumer’s income is $40,000, and the quantity demanded of a good is 2,000. The income elasticity of demand is +0.60. If the consumer’s income changes to $41,000, what is the new quantity demanded?

Exercise 4.3: Income Elasticity of Demand

What is the income elasticity of demand for a laptop computer? Assume there is no inflation from 20X8 to 20X9 and all other items are held constant, such as the consumer’s assets and relative prices of goods.

                    20X8                20X9
●    Income             $50,000            $55,000
●    Price             $2,000                 $2,000
●    Quantity        1,000                1,100

Exercise 4.4: Linear Demand Curve

If the demand curve is Q = α + βP, what is the elasticity as a function of P?

Exercise 4.5: Shape of Elasticity Curve

Several of the illustrative test questions and practice problems discuss whether the price elasticity of demand increases or decreases (or remains constant) as the price increases. The shape of the price elasticity of demand curve is not the same for all goods, and it is not the same for a population vs an individual. Explain whether you would expect the price elasticity of demand to increase or decrease in absolute value as the price increases. A one paragraph explanation is sufficient for the homework, though you may expand on your answer to explain different scenarios that occur in practice.


Question: What is this exercise asking?

Answer: Bread has a downward sloping demand curve. If bread is cheap, such as 50¢ a loaf, consumers buy all they can eat. If bread is 40¢ a loaf, they still buy all they can eat. What is the price elasticity of demand in this price range? But if bread is expensive, such as $10 a loaf, consumers may buy one loaf of bread a week. If bread is $20 a loaf, consumers may buy one loaf of bread a month. What is the price elasticity of demand in this range?]

Okay,the homework is asking for me to do Linear Demand Curves. However, the seventh edition doesn't even cover this topic.(Not even in the index) I have looked at the concepts and overviews and the other supporting material in this section and I am coming up with nothing.

NEAS, please advise what I should do about this problem and do I need to know this for the final exam?

[NEAS: Demand curves are discussed on pages 2-4 of Landsburg’s text (seventh edition). A linear demand curve is a demand curve which is linear, such as Quantity = A – B × Price.

Real supply and demand curves are not linear.

Real demand curves are asymptotic to both axes, but a linear demand curve intersects both axes.

In the short run, real supply curves are convex, since quantity is limited by production capacities.

In the long run, real supply curves are concave, since firms build new plans if demand is high.

Landsburg uses linear supply and demand curves for almost all the examples in his text. You solve simultaneous linear equations to find the equilibrium price and quantity.

This course also uses linear supply and demand curves for the final exam problems. The practice problems show how to

evaluate equilibrium quantities and prices using linear supply and demand curves

calculate the consumers’ surplus and producers’ surplus with these curves

adjust the curves for sales taxes and excise taxes

determine the price elasticities of supply and demand for these curves

The textbook assumes knowledge of high school algebra for the mathematical exercises. The on-line course assumes you can integrate and differentiate linear curves.]

Now I am unable to locate information about Constant Price Elasticity either in the seventh edition.

NEAS, please advise. Is anyone else having difficulties finding the required information that we need in the seventh edition????

[NEAS: Landsburg discusses price elasticity of demand in chapter 4. Landsburg uses discrete illustrations. This course assumes you can differentiate the supply and demand curves.

The elasticities vary by the market price and quantity. In particular, the elasticities are not constant for linear supply and demand curves. For the final exam, know how the elasticity varies by high vs low quantity and high vs low price for linear curves.Illustration: An exam problem may say the demand curve is linear and give the elasticities at P = $10 and P = $11. You are asked to derive the elasticity at another point, such as P = $9 or P = $12.

Landsburg discusses an example with constant price elasticity of demand on pages 104-105 of the seventh edition. Part A of this exercise requires simple calculus to differentiate a hyperbola. The final exam assumes can you differentiate a hyperbola.Illustration: An exam problem may give a demand curve as Q × P = 100 and ask for the price elasticity of demand. If you have trouble with this, review pages 104-105 of the text.

Many exam problems give the price, quantity, and elasticity at one point and derive the quantity at a nearby point. The exam problem assumes the elasticity is constant between these two points.Illustration: At a price of $100, 5,000 units are demanded. If η (the elasticity) = –1.5, how many units are demanded at a price of $101? (Or: how many units are demanded at a price of $98? Or: at what price are 5,075 units demanded?)

The exam problem assumes the elasticity of –1.5 can be used for a change of $1. In truth, if the elasticity is –1.5 at P = $100, the elasticity for move up one dollar differs from the elasticity for moving down one dollar. The effects are not material, and the exam problems do not specify the range for the average elasticity.]

I am still confused about problems 4.4 and 4.5.  Where can I go to have a clearer explantion?  Also, don't we need to know if the good is normal or inferior?

Thanks

[NEAS: Problem 4.4 gives a demand curve; compute the price elasticity of demand, using the definition (∂Y/∂X * X/Y). Problem 4.5 asks exactly what you say: how does the price of a good affect whether it might be normal or inferior?]

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