Chapter 3. Demand Theory
 

1.Textbook questions #:  4, 5, 6, 7, 16, 21, 22, 24, 27, 29.

2. True/False

1. Since the real price for automobiles has increased but the quantity demanded has also increased over recent years, the demand curve for automobiles must be positively sloped.

2. There is no money illusion for the demand curve x₁=5M(p₂/p₁)^1/2.

3. All inferior goods are Giffen goods.

4. All Giffen goods are inferior goods.

5. If the income elasticity of a good is negative, the demand curve of that curve must be negatively sloped.

6. If, at the utility maximizing bundle of good 2 and good 1, the MRS of good 2 for good 1 is greater than p₁/p₂, then good 1 is an inessential good.

7. Suppose that an individual consumes only two goods, good 1 and good 2. If the price of good 1 rises, with all else constant, and the price elasticity of demand for good 1 is -0.7, then the quantity of good 2 will increase.

8. If an individual's income is the same before and after an excise tax is imposed on good 1 and the demand for good 1 is elastic, the excise tax will lead to an increase in spending on other consumer goods.

9. Since a decrease in the price of one unit along a linear demand curve will result in an increase in the quantity demanded by a constant amount, the price elasticity is constant for all quantities along a linear demand curve.

10. Let good 1 be on the horizontal axis, and let the quantity of the composite commodity be on the vertical axis. Then, if the (absolute value of the) price elasticity of demand for good 1 is less than 1, the price consumption line is negatively sloped.

11. Along a consumer's budget line, money income is constant.

12. A commodity bundle lying below a consumer's budget line must be inferior to all bundles lying on the budget line.

13. Assume that a certain individual consumes only goods 1 and 2. If the prices of good 1 and good 2 double and his income doubles, then the quantity demanded for goods 1 and 2 will not change.

14. If a decline in the prices of agricultural products results in a reduction in the consumption of these goods by farmers, then these products must be inferior goods.

Answers:  1.F   2.F    3.F    4.T    5.F     6.F    7.F
                8.T   9.F   10.F  11.T  12.F  13.T  14.F
 

2. Short Questions.

1. Sally's demand for apples is given by x₁=M/p₁. Graph her demand curve, and calculate the price elasticity of demand for apples.

2. Suppose that a consumer's preferences are given by  U = ln x₁ + x₂, and his budget constraint is given by p₁x₁ + p₂x₂ = m  where x₁ and x₂ are goods, p₁ is the price of x₁, and m is the consumer's income. Find the demand functions for x₁ and x₂. Is x₁ an ordinary good? Why or why not?

3. Cari Obeck's demand function for tuna is given by: q=2m/5p  where q is the number of cans of tuna demanded, p is the price of tuna, and m is her income. Suppose Cari's income is $100. If the price of tuna falls from $5 to $4, what happens to the demand for tuna?

4. Pat Impecunious spends all her money on two goods: bologna and white bread. Can both of them be inferior? Explain.

5. Susan Ng's preferences over bowls of french fries (x₁) and pints of ice cream (x₂) are given by: U=x₁²+x₂²
The price of french fries is $2 a bowl while the price of ice cream is $3 a pint. Her income is $8. At her optimal choice, how many bowls of fries will she buy? How many pints of ice cream?

6. Explain what is meant by the terms demand function and Engel curve and for each of the following state whether the function is a demand function, an Engel curve, both or neither.
  x₁ = m - p₁/p₂
  m = p₁x₁
  x₂ = m² - x₁/p₁p₂

7. Sally consumes two goods, X and Y. Her utility function is given by the expression U(X,Y) = X^0.4Y^0.6
The current market price of X is $20 per unit, while the market price of Y is $100 per unit. Sally's current income is $10,000.
  a). Calculate Sally's demand for X as a function of prices and incomes. Is good X normal? Please show all work.
  b). How much X and Y will Sally demand at current market prices? What will Sally's utility be with that consumption?
  c). Find the income elasticity and the price elasticity of the Marshallian demand for X.

8. If the compensated demand curve for peanuts is steeper than the ordinary demand curve, then
  i). peanuts are a normal good
 ii). peanuts are an inferior good
iii). we do not have enough information to decide whether peanuts are normal or inferior.
Select one of (i), (ii) or (iii) and support your answer with diagrams and an explanation.

Answers:  1. E₁₁=-1
                2. x₁*=p₂/p₁; x₂*=(m-p₂)/p₂; Yes because the demand is downward sloping.
                3. The demand for tuna will increase from 8 to 10 cans.
                4. No. If Pat's income increases she cannot decrease the consumption of both goods. The Budget costraint will not be satisfied. At  least one of the goods must be normal.
                5. x₁*=4 and x₂*=0. Note that the indifference curves are not convex, therefore the tangency is not the optimal solution. In this case we have a corner solution.
                6. demand curve, Engel curve, neither (because of the x₁ in the formula)
                7. a) x=0.4M/p_x; y=0.6M/p_y; Yes. b) x=200, y=60. c) E₁₁=-1, E_1M=1.
                8. Normal good.If the compensated demand curve for peanuts is steeper than the ordinary demand curve, this means that the TE is larger than the SE., and both are negative. Therefore IE is also negative.
 

3. Long Questions.

1.  Mary has an income of $10 per week, which she spends on Marmite which costs $4 a jar, and bread, which costs $2 per loaf.
  a) Draw Mary's budget line? What is the slope of her budget line?
  b) Show the effect on the budget line of halving the price of Marmite to $2 per jar.
  c) Show that a 50 per cent reduction in the price of both Marmite and bread (to $2 a jar and $1 per loaf) has the same effect on Mary's budget line as a doubling of Mary's income to $20 per week.
  d) Suppose the government, due to a national shortage of brewers yeast (the main ingredient in Marmite) decides to ration Marmite consumption to one jar per week. Show the effect of the rationing on the original (part a) budget constraint.

2.  Geoff Howard's well-being depends upon his consumption of milk (in pints, x₁) and video games (x₂). His utility function is given by: U = 3lnx₁+x₂.  Calculate his demand for milk, his demand for video games, and his optimal choice when p₁=$3/pint, p₂=$2/game and m=$14.
Now suppose the government subsidized Geoff's milk by $2 per pint, so the price of milk fell from $3 to $1.
a) Calculate
    (i) how much milk Geoff would demand at the subsidized price
   (ii) How many video games he would demand and
  (iii) His level of utility
  (iv) The cost of the subsidy to the government.
b) If the government gave Geoff the amount calculated in part (a - iv) in cash (leaving the price of milk at its original level of $3) how much milk would he demand, how many video games, and what would his utility be?
c) Draw a diagram showing the budget constraint with the subsidy, the budget constraint with the cash transfer, Geoff's optimal choice under the two schemes, and the cost of each program..

Answers:
               1. a) slope is -2 (with Marmite on the horizontal axis); b) rotates outward; d) the budget line will consist of two parts: for any quantity of Marmite lass than 1 will be the same as before rationing and for then at 1 will be a vertical line. Basically any quantity more than 1 is not available anymore.
               2. x₁=3p₂/p₁ = 2; x₂=(M-3p₂)/p₂ = 4. a) i)6, ii)4,  iii)3ln6+4, iv)$12. b) milk=2, video=10, U=3ln6+10.