Problem Set 2

Due by 11:59 PM Monday February 20 via by Blackboard Assignments

Please read the instructions for completing homeworks.

Answers

Concepts and Critical Thinking

Please answer the following questions briefly (1-3 sentences). Use examples as necessary. Be sure to label graphs fully, if appropriate.

Question 1

Describe, in your own words, the (i) price effect, (ii) real income effect, and (iii) substitution effect from a price change.

Question 2

Under what conditions can the law of demand be violated (however theoretical)?

Question 3

For each of the following pairs, which of the two goods is more likely to have a low price elasticity of demand (less elastic) and why?

Part A

Demand for tangerines vs. demand for fruit

Part B

Demand for beef next month vs. demand for beef over the next decade

Part C

Demand for Exxon gasoline at the corner of 7th and Grand vs. demand for gasoline in the entire city

Part D

Demand for insulin vs. demand for vitamins

Question 4

Suppose that, holding prices constant, Alice has preferences over the number of books she purchases, illustrated in the table below.

Income	Books
$5	5
$10	6
$15	20
$20	25
$25	26
$30	10
$35	9
$40	8
$45	7
$50	6

Draw a smooth approximation of Alice’s Engel curve for books, and indicate the range(s) of income over which books are normal and/or inferior goods.

Quantitative Applications

Show all work for calculations. You may lose points, even if correct, for missing work. Be sure to label graphs fully, if appropriate.

Question 5

Steve spends his disposable income on meals at restaurants $(r)$ and paperback novels $(n)$ . His usual restaurant meal costs $25, and paperback books cost $8. When Steve’s monthly income is $240, he goes out to eat 8 times and purchases 5 books. When his income rises to $282, he goes out to eat 10 times and purchases 4 books.

Part A

Calculate the income elasticity for meals at restaurants $(r)$ . Is this an inferior, necessity, or luxury good?

Part B

Calculate the income elasticity for paperback novels $(n)$ . Is this an inferior, necessity, or luxury good?

Question 6

Kendra buys eggs $(e)$ , bagels $(b)$ , and coffee $(c)$ for breakfast for the week.

Part A

When eggs are $2/carton, she buys 5 bagels. When the price of eggs falls to $1/carton, she buys 4 bagels. Calculate the cross-price elasticity between eggs and bagels. Are they complements or substitutes for Kendra?

Part B

When eggs are $2/carton, she buys 3 cups of coffee. When the price of eggs falls to $1/carton, she buys 6 cups of coffee. Calculate the cross-price elasticity between eggs and coffee. Are they complements or substitutes for Kendra?

Question 7

Sketch a graph showing an increase in the price of a good (on the horizontal axis, e.g. $x$ if you want). Indicate (i) the (real) income effect, (ii) substitution effect, and (iii) price effect on the graph. Labeling points and merely describing each of the three effects as a movement between specific points is sufficient.

Question 8

The demand for gym memberships is given by $q_{D} = 500 - 5 p$

Part A

Write the inverse demand function.

Part B

Calculate the price elasticity of demand at a price of $80. Is this relatively elastic or relatively inelastic?

Part C

What is the total revenue at a price of $80?

Part D

Calculate the price elasticity of demand at a price of $10. Is this relatively elastic or relatively inelastic?

Part E

What is the total revenue at $10?

Part F

At what price is demand unit elastic, i.e. $ϵ_{D} = - 1$ ?

Part G

What is the total revenue at the price you find in part (f)?