1

QUEENS COLLEGE, ECONOMICS 703, Take-home Prof. DohanOct 4, 2004

Name______Date Taken ______Start:______.End______

Phone Number ______, Year____, Major ______, E-mail______

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. 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. 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?

______

3. 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.

1

1

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)

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.

4. 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)

  1. U(x, y) = 3x + y, with MUx = 3 and MUy = 1.
  1. U(x, y) = x0.4y0.6 with MUx = 0.4(y0.6/x0.6) andMUy = 0.6(x0.4/y0.4)
  1. U(x, y) = x2 + y2, with MUx = 2x and MUy = 2y.
  1. Is the assumption that “more is better” satisfied for both goods.
  1. Does the marginal utility of x diminish, remain constant or increase as the consumer buys more x? Explain
  1. What is the MRSxy?
  1. Is the MRSx,y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve.
  1. 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.
  1. On the same graph draw a second indifference curve U2, with U2>U1.

5. 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 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

6. 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.

7. Suppose that the following graph represents the optimal consumption bundle 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.
  1. 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.)
  1. 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.

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.

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 all OF THE FOLLOWING: Use the back of the paper if more space is needed.

A. 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 – 0.04PQs = 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 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?)