ECON 100 Tutorial: Week 4

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ECON 100 Tutorial Week 4

• www.lancaster.ac.uk/postgrad/murphys4/
• s.murphy5_at_lancaster.ac.uk
• office LUMS C85

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Outline for this weeks tutorial

• Past exam question ( from last week) 5 min.
• Question 1 2 min.
• Question 2 3 min.
• Question 4 5 min.
• Question 5 10 min.
• Question 7 20 min.
• Solutions for Q6 and Q8 are in the slides (and on
  Moodle) please review them and email me or come
  to office hours if you have questions, but we
  will not be going over them in tutorial.

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Past exam question from last week

•  

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Suppose D120-4P. Find the price elasticity at a
price of 10 and at a price of 20. Use the
standard mathematical method, not the midpoint
method.

1. -0.2, -2, respectively
2. -0.5, -2, respectively
3. -0.5, -4, respectively
4. Not possible to say without knowing what the
   corresponding level of demand is.

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An Inferior Good

1. Is a Giffen good
2. Has a positive income elasticity of demand
3. Has a negative income elasticity of demand
4. Has an upward sloping demand function

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Suppose a demand curve is written D60-3P. Find
the intercept and slope of the corresponding
inverse demand curve.

1. Slope of -20, intercept of 3
2. Slope of -1/3, intercept of 20
3. Slope of -3, intercept of 20
4. Slope of 1/3, intercept of 60

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Suppose D200-2P and S204P. What is the
equilibrium price and quantity?

1. P20, Q100
2. P30, Q140
3. P50, Q220
4. P40, Q180

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Question 1

• Assuming an indifference curve which is convex to
  the origin, what can this tell us about a
  consumers marginal rate of substitution between
  coffee and muffins?

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Question 2

• Explain why the consumers optimal choice occurs
  where the marginal rate of substitution (MRS) is
  equal to the relative price of the two goods.

The optimal choice is where one indifference
curve is touching the budget constraint at
exactly one point (where the indifference curve
is tangent to the budget constraint). The MRS is
the same thing as the slope of the budget
constraint. If a line is tangent to another
line, their slopes are equal at the point of
tangency.
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Question 3

•  

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Question 4

• Would the assumption that goods are perfect
  substitutes be valid in a study of intertemporal
  food purchases?

Perishable foods in one time period are not a
perfect substitute for food in another time
period.
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Question 5(a)

• Use a diagram to distinguish between the income
  and substitution effects of a change in the price
  of muffins when the price of coffee stays
  constant. Assume both goods are normal goods.
• So, what are a substitution effect and an income
  effect?
• First, we draw our original budget constraint,
  original indifference curve, and the new budget
  constraint.
• Next, we can find the substitution effect, the
  movement along the indifference curve, to a point
  whose MRS is equal to the slope of the new budget
  constraint.
• Finally, we can find the income effect which
  will move us to a new indifference curve on the
  new budget constraint this depends on whether
  our good whose price changed is a normal,
  inferior or giffen good.

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Question 5(b)

• Suggest an example of an inferior good. Use a
  diagram to distinguish between the income and
  substitution effects of a change in the price of
  the inferior good.

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Question (c)

• Suggest an example of a Giffen good. Use a
  diagram to distinguish between the income and
  substitution effects if a change in the price of
  the Giffen good.

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Question 6(a)

• Suppose a consumer only buys two goods hot dogs
  and hamburgers. Suppose the price of hot dogs is
  1, the price of hamburgers is 2, and the
  consumer's income is 20. Plot the consumer's
  budget constraint. Measure the quantity of hot
  dogs on the vertical axis and the quantity of
  hamburgers on the horizontal axis. Explicitly
  plot the points on the budget constraint
  associated with the even numbered quantities of
  hamburgers (0, 2, 4, 6 . . .).

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hot dogs 1, hamburgers 2 consumer's income
20.
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Question 6(b)

• Suppose the individual chooses to consume six
  hamburgers. What is the maximum amount of hot
  dogs that he can afford? Draw an indifference
  curve on your diagram that establishes this
  bundle of goods as the optimum.
•  
• Answer Eight.

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Question 6(c)

• What is the slope of the budget constraint?
• Rise over run 2/1. This is also the price ratio
  of price of hamburgers to price of hot dogs
  2/1. The slope of the indifference curve is
  also 2/1. (Note all of these slopes are
  negative.)
• What is the slope of the consumer's indifference
  curve at the optimum?
• What is the relationship between the slope of the
  budget constraint and the slope of the
  indifference curve at the optimum?
• At the optimum, the indifference curve is tangent
  to the budget constraint so their slopes are
  equal.
• What is the economic interpretation of this
  relationship?
• Thus, the trade-off between the goods that the
  individual is willing to undertake (MRS) is the
  same as the trade-off that the market requires
  (slope of budget constraint).

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Question 6(d)

• Explain why any other point on the budget
  constraint must be inferior to the optimum.

Because the highest indifference curve reachable
is tangent to the budget constraint, any other
point on the budget constraint must have an
indifference curve running through it that is
below the optimal indifference curve so that
point must be inferior to the optimum.
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Question 7(a)

• Suppose the price of a magazine is 2, the price
  of a book is 10, and the consumer's income is
  100.
• Which point on the graph represents the
  consumer's optimum X, Y, or Z?
• What are the optimal quantities of books and
  magazines this individual chooses to consume?
• Answer Point Z.
• 25 magazines and 5 books.

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Question 7(b)

• Suppose the price of books falls to 5. What are
  the two optimum points on the graph that
  represent the substitution effect (in sequence)?
• Answer From point Z to point X.
• What is the change in the consumption of
  books due to the substitution effect?  
• Answer From 5 to 8 books.

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Question 7(c)

• Again, suppose the price of books falls to 5.
  What are the two optimum points on the graph that
  represent the income effect (in sequence)?
• Answer From point X to point Y.
• What is the change in the consumption of
  books due to the income effect? From 8 to
  6 books.

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Question 7(c) ctd.

• Is a book a normal good or an inferior good for
  this consumer? Explain.
• Books are inferior because an increase in
  income decreases the quantity demanded of books.
  

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Question 7(d)

• For this consumer, what is the total change in
  the quantity of books purchased when the price of
  books fell from 10 to 5?
• Answer The quantity demanded increased from five
  books to six books.

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Question 7(e)

• Use the information in this problem to plot the
  consumer's demand curve for books on a diagram.

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Question 8(a)

• Explain why if two goods (called 1 and 2) are
  perfect substitutes then their utility function
  is linear for example, Uq1q2.
• Answer Rearrange this so q2 is on the
  left-hand-side and everything else is on the
  right.
• The slope is -1 (ie 45o downward sloping) and the
  intercept on the q2 axis is U.

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Question 8(b)

• Show, in this case, that demand for good 1 is
  Y/p1 if p1ltp2 and 0 otherwise (where Y is income)
  while the demand for good 2 is q2Y/p2 if p2ltp1
  and 0 otherwise.
• Answer The budget constraint says that income,
  Y, equals expenditure on good 1 plus expenditure
  on good 2. So p1q1 p2 q2 Y.
• You can rearrange this to get q2 on the left hand
  side and everything else on the right. That is
• q2Y/p2 (p1/p2)q1 .
• Since prices and income are fixed this is a
  linear equation and the slope of this budget
  constraint is just -(p1/p2).
• This is steeper than 45o if p1gtp2 and shallower
  if p1ltp2 .
• So if p1gtp2 then the consumer only buys the
  cheaper good 2 and so q2Y/p2 and if p2gtp1 then
  the consumer only buys the cheaper good 1 and so
  q1Y/p1.

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Question 8(c)

• It is common in many economic applications to
  assume that a utility function is quasi-linear.
  An example of quasi-linear is the equation U
  q2?q1. Show that this implies that indifference
  curves are parallel.
• HINT The indifference curve can rewritten as
  q2U-?q1 and you can find the slope of this
  relationship by applying the rule on slide 9 of
  lecture 6 and noting that ?q1 q1½.
• Answer Applying the rule, the slope of q2
  U-q1½ is (½) q1-½, or - 1/2?q1, which depends
  only on q1, not on Y. So whatever the value of Y
  the slope is the same.

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Question 8(d)

• The demand curve can be found by equating the
  slope of the budget constraint to the slope of
  the indifference curve. Do this and show that q1
  does not depend on Y, but that q2 does.
•  
• Answer the demand curve is defined by
• the price ratio MRS
• -(p1/p2) -1/2?q1
• so ?q1 p2/2p1
• or q1 p2/p12/4 - which does not depend on
  Y.
• Substitute this into the budget constraint and
  solve to get q2 on the left hand side to find
  that that the demand for good 2 is given by
• q2(Y/p2)-(p2/4p1), which does depend on Y.

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Question 8(e)

• What happens to the demand for q2 if Ylt p22/4p1?
  And what happens to the demand for q1 when this
  happens?
•  
• Answer If Y p22/4p1 then q20. This remains
  true for lower values of Y. If q20 then Yp1q1
  and so q1Y/p1 so everything is spend on good
  1.

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Next Week

• Tutorial 5 Worksheet
• Practice exam questions in tutorial.
• Access past exams here http//www.lancaster.ac.uk
  /sbs/registry/Exams/PastPapers/PastPapers.htm
• You will need to select a year, then select ECON
  100 or ECON 101. You will be looking at
  approximately the first 10 questions from each
  years exam.

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