Download Eco205 Mid Term - Professor Dohan`s Website, Queens College

QUEENS COLLEGE, ECONOMICS 205, Mid-Term Prof. Dohan
1
March 21, 2002
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There are 10 questions. Work steadily. Allocate your time carefully. Do try to answer every question, however. Please be fair to
your fellow students. Remember that this is a closed book exam. No books, no notes and no similar study aids are permitted. No
talking. Do not facilitate or permit other students to benefit from your exam and do not represent other's work as your own. Failure
to observe these standards will automatically result in at least an F for the course. 1 point for each question unless otherwise
stated.
Instead of letting you choose 2 out of 3 in four groups, I have made most questions mandatory (usually the
easier ones or from early quizzes or went over in class). Questions 4 and 10 have choices. You can do the
other ones for extra credit (at 5 points each)
1. (2.3bk) The demand and supply curve for coffee are given by
Qd = 600 – 2P
and Qs = 300 + 4 P
a) Plot the supply and demand curves (carefully)
on a graph and show where the equilibrium
occurs. (But remember you only need to use
two points for plotting a straight line equation).
b) Using algebra, determine the market equilibrium
price and quantity of coffee. (It should give the
same answer as in part a.)
2. (Wkbk21) Suppose that the demand for pizza in the U.S. is as follows:
Q = 200 – 5Pp - .25 Pb + 50D +01I
Where: Pp is the average price in dollars per medium-sized pizza, Pb is the average price of beer in
dollars per six pack, D is a “football season” variable which takes the value 1 when it is football
season and takes the value 0 other wise, and I is disposable personal income.
Elasticity: In the neighborhood of Pp=$8, Pb = $4, D = 1 and I =$10,000.
a) What is the price elasticity of demand for pizza?
b)
What is the cross-price elasticity of demand for pizza with respect to beer?
c)
What is the income elasticity of demand for pizza?
d)
What happens to the demand for pizza when the price of beer goes up?
e)
Are pizza and beer demand substitutes or demand complements.
Demand Curves
a) Draw the demand curve for pizza supposing that
Pb = 4, D=1 and I = $10,000.
b) Now, draw the demand curve for pizza
supposing that all the values of the variables are
the same except that D=0. Compare the two
demand curves. What has changed?
______________________________________
c) Now, draw the demand curve for pizza
supposing that Pb = 4, D=1 and I = $12,000.
compare this to the first demand curve in a).
What has changed?
______________________________________
d) Now, draw the demand curve for pizza
supposing that Pb = $4, D=0, and I = $12,000
and compare this to the first demand curve in
(a). What has changed?
______________________________________
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3. (3.2 bk) For the following sets of goods draw two indifference curves U1 and U2, with U2 > U1.
Draw each graph, place the amount of the first good on the horizontal axis.
a. Hot dogs and chili (the consumer likes both
and a diminishing marginal rate of
substitution of hot dogs for chili)
b. Sugar and Sweet’N Low (sugar substitute)
(the consumer likes both and will accept an
ounce of Sweet’N Low or an ounce of sugar
with equal satisfaction)
Hot dogs
c. Peanut butter and jelly (the consumer likes
exactly 2 ounces of peanut butter for every
ounce of jelly)
d. Nuts (which the consumer neither likes nor
dislikes and ice cream (which the consumer likes)
e). Apples (which the consumer likes) and liver
(a meat, which the consumers dislikes.
Nuts
Sugar
Peanut Butter
Apples
4. 3.? Bk Choose only one of the utility functions below and then answer all the following questions for
that utility function.:
Note: Circle the letter (a, b, c) of which utility function you are using.
Prove or show how you got your answers. (“Yes or no” or a number is not a complete answer)
a. U(x, y) = 3x + y, with MUx = 3 and MUy = 1.
b. U(x, y) = x0.4y0.6 with MUx = 0.4(y0.6/x0.6) and MUy = 0.6(x0.4/y0.4)
c. U(x, y) = x2 + y2, with MUx = 2x and MUy = 2y.
a. Is the assumption that “more is better” satisfied for both goods.
b. Does the marginal utility of x diminish, remain constant or increase as the consumer buys
more x? Explain
c. What is the MRSxy?
d. Is the MRSx,y diminishing, constant, or increasing as the consumer substitutes x for y along
an indifference curve.
e. On a graph with x on the horizontal axis and y on the
vertical axis, draw a typical indifference curve (it need
not be exactly to scale, but it needs to reflect accurately
whether or not there is a diminishing MRSx,s). Also
indicate on your graph whether the indifference curve
will intersect either or both axes. Label the curve U1.
f. On the same graph draw a second indifference curve
U2, with U2>U1.
5. 4.3 bk Jane likes hamburgers (H) and milkshakes (M). Her indifference curves are bowed in
toward the origin and do not intersect the axes. The price of a milkshake is $1 and the price of a
hamburger is $3. She is spending all her income on the basket she is currently consuming, and her
marginal rate of substitution of hamburgers is 2.
5.a Is she at the optimum? Explain using the MRS and Ph/Pm t why or why not she is at the optimum.
5.b On a graph of several indifference curves
and a budget line with H on the horizontal
and M on the vertical, show why or why
not.? Illustrate on the graph at what point
Jane is.
5c If she is not, should she buy fewer hamburgers and more milkshakes, or the reverse. Illustrate on graph
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6. 5.6 bk Rick purchases two goods, food
and clothing. He has a diminishing marginal
rate of substitution of food for clothing. Let
x denote the amount of food consumed and
y the amount of clothing. Suppose the price
of food increases from Px1 to Px2. On a
clearly labeled graph, illustrate the income
and substitution effect of the price change
on the consumption of food by drawing a
new indifference curve that illustrates each
of the following cases.
Case 1: Food is a normal good
Case 2: The income elasticity of
demand for food is zero.
Case 3: Food is an inferior good, but
not a Giffen good.
Case 4: Food is a Giffen good.
I
II
Px1
Px1
Food
Food
III
IV
Px1
Food
Px1
Food
7. 4.1 wbk Suppose that the following graph
represents the optimal consumption bundle 80
of a typical consumer when
 an income of 80,
 prices of Px = 1,
 Py = 1 and
 utility U = xy
 marginal utility MUx = y
 and MUy = x)
1. Now, let income remain fixed but let prices
rise so that the new prices are Px = 2, Py = 4.
Illustrate the new budget line and draw a
sample indifference curve to show the new
optimal bundle.
80
2. Let income be indexed to the cost of living so that the budget line shifts out just enough that the
old bundle (at the original prices, above) is just affordable. In other words, let income increase
to 240 Is the old bundle still the optimal choice at this new income level and at the new prices?
Has utility increased above that of the original consumption bundle (explain and illustrate
answer on graph.)
x
3. Suppose that prices are now Px = 2, Py = 2, and income has increased to 160 (so that both prices and
income have exactly doubled over their original levels). Is that old bundle optimal now? Has utility
increased above that of the original consumption bundle. Illustrate and explain.
8. 4.2 wk (From the quiz)
Let the budget constraint of a consumer by PxX + PyY = I.
a) let a consumption tax of t per unit be placed on good x. Write the new budget constraint.
b) let a subsidy of s% be placed on y. Write the new budget constraint.
c) Let a lump sum tax of “Tx” be applied to income. Write the new budget constraint.
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9. 5.5 wkbk. Inma is considering how many hours to work. She has a backward-bending supply of
labor and leisure is a normal good for her. Explain and illustrate your answer on a graph.
a) A new government program imposes a $1 wage
tax (so that workers are paid w-1 per hour rather
than w per hour). Will Inma increase or
decrease her hours worked in response to the
tax?
b) An alternative government program imposes a
$1 per head tax (i.e., a $1 tax paid per person,
regardless of income or wage level). Will Inma
increase or decrease her hours worked in
response to the tax?
10. ANSWER ONE OF THE FOLLOWING: Use the back of the paper if more space is needed.
A. (Wkbk23) Most Californians use cars daily to commute to work and for their transportation
needs. The increasing price of auto insurance, however, has led to consumer discontent. In order to
hold costs down the auto insurance industry has promoted tort law reform, which would reduce
insurers’ costs by limiting when and for how much people can sue each other after an accident. An
alternative proposal by a pro-consumer group is to limit the price insurers can charge to 75% of the
current price. The current demand and supply curves for auto insurance (before any program is
enacted) are:
Qd = 100 – 0.04P
Qs = 0.06P – 20
Where P is the price of auto insurance and Q is the quantity, in millions.
a) What are the current market price and quantity in the market?
b) Under the pro-consumer plan, a price ceiling is imposed where the new maximum price is
75% of the equilibrium price obtained in (a). What are the new price and quantity in the
market?
c) The reduction in insurers’ cost under the industry-sponsored plan will change the supply
curve to
Qs= 0.06P
What is the new price and quantity in the market under this proposal?
B. The current price in the market for bananas is $0.40 per pound. At this price, 1 million pounds
are sold per year in Smalltown, U.S.A. Suppose that the price elasticity of demand is –2 and the
short-run price elasticity of supply is 0.05. Solve for the equations of demand and supply, assuming
that demand and supply are linear.
C 2.9 bk Suppose that the market for air travel between Chicago and Dallas is served by just two
airlines, United and American. An economist has studied this market and has estimated that the
demand curvers for round-trip tickets for each airlines are as follows:
QdU = 10000 – 100PU + 99PA (United’s demand)
QdA = 10000 – 100PA + 99PU (United’s demand)
Where PU is the price charged by United and PA is the price charged by American.
a) Suppose that both American and United charge a price of $300 each for a round-trip ticket
between Chicago and Dallas. What is the price elasticity of demand for United flights
between Chicago and Dallas.
b) What is the market-level price elasticity of demand for air travel between Chicago and
Dallas when both airlines charge a price of $300. (Hint: Because United and American are
the only two airlines serving the Chicago-Dallas market, what is the equation for the total
demand for air travel between Chicago and Dallas, assuming that the airlines charge the
same price?)