Test #1 Answers

Multiple Choice:

1=c; 2=a; 3=d; 4=a; 5=b; 6=c; 7=a; 8=d; 9=a; 10=b; 11=c; 12=d; 13=d; 14=b; 15=c; 16=b; 17=a; 18=c; 19=b; 20=d.

Question 1: Basics of Supply and Demand

1a)Suppose we are analyzing the market for potatoes. Sketch a quick supply and demand diagram to show which curve will shift and state the resulting impact on the equilibrium price and quantity of each of the following events affecting the potato market (6 points):

  1. Potatoes are now considered by doctors to be the most healthy vegetable to eat: D shifts right, P increases, Q increases
  1. There is a decline in the amount of land dedicated to growing potatoes: S shifts left, P increases, Q decreases
  1. The price of rice falls: Rice is a substitute; D shifts left, P decreases, Q decreases
  1. Scientists discover a new method of growing potatoes which dramatically increases farmers’ productivity: S shifts right, P decreases, Q increases

1b)Suppose a new discovery in computer manufacturing has made production cheaper. In addition, the popularity and usefulness of computers continues to grow. Use supply and demand analysis to predict how these shocks will affect equilibrium price and quantity of computers. Is there enough information to determine if market prices will rise or fall? Explain why or why not (4 points).

The increase in demand will cause P and Q to rise; the increase in supply will cause P to fall while Q increases. Thus, the two effects on price work in opposite directions. If the supply effect dominates the demand effect, then prices fall (as shown here). If the demand effect dominates, prices will rise. We don’t know which effect dominates, given the current information, so can’t perfectly predict the change in price.

1c)The market for gravel has been estimated to have these supply and demand relationships, where P = $ price per ton, and Q = sales per week in tons:

SupplyP = 10 + 0.01Q

DemandP = 100 – 0.01Q

  1. Determine the equilibrium price and quantity (2 points)

10 + 0.01Q = 100 – 0.01Q. Thus, 0.02Q = 90

Q = 4,500 tons/week; P = 10 + 0.01(4,500) = $55/ton.

  1. Determine the amount of shortage or surplus that would develop at P = $40/ton (2 points).

At P = $40/ton, Qd = 40 = 100 – 0.01Q or Qd = 6,000 tons/week. Qs = 40 = 10 + 0.01Q or Qs = 3,000 tons/week. The shortage is 3,000 tons/week.

  1. What would be the impact on the market if the government set a price floor of $70 per ton of gravel? (1 point)

The price floor is binding as it is above the equilibrium price. There would be excess supply of 3000 tons of gravel. Qd = 3000 tons; Qs = 6000 tons.

Question 2: Consumer Behavior

2a) An island economy produces only two goods: coconuts and pineapples. Four people (A, B, C, and D) live on the island. Given the following preferences, construct a representative indifference curve for each of the individuals with pineapples on the vertical axis and coconuts on the horizontal axis. Discuss the shape of the indifference curves and relate them to the MRS. (8 points)

Ahas a strong preference for pineapples.

Bhas a strong preference for coconuts.

C has a life-threatening allergy to pineapplesso assigns no value to them.

D will only consume pineapples and coconuts in the fixed proportion of one P to one C.

The MRS measures the incremental number of pineapples the consumer will forego to get a one unit increase in coconuts.A has relatively flat ICs (needs lots of C to compensate for the loss of P) so A’s MRS is low. B has relatively steep ICs (needs few C to compensate for the loss of P) so B’s MRS is high. C’s MRS is infinite (as utility is not affected by P, he will give up all P (infinite) to increase C). D’s MRS is infinite when Qp>Qc, zero when Qc>Qp.

2b) George has $50 to spend on clothing, C, and food, F, where C costs $10 per unit and F costs $5 per unit. Putting F on the horizontal axis, draw George’s budget line and an indifference curve such that he buys2F. Assuming Martha has the same income and faces the same prices, but buys6F, draw her indifference curve on the same diagram. In equilibrium, what is the MRS of F for C for George? And for Martha? (3 points)

In equilibrium, both George’s and Martha’s MRS = Pf/Pc = 5/10 = ½.

2c) Peter consumes goods X and Y and spends $25 per week. The per unit price of X = $3; the per unit price of Y = $2. Peter’s utility function can be written as U(X,Y) = 0.5XY. This implies that the MUX = 0.5Y, and the MUY = 0.5X.

  • Write the expression for Peter’s marginal rate of substitution between X and Y. (1 point): MRS = MUX/ MUY= 0.5Y/0.5X = Y/X
  • Write the expression for the budget line. (1 point): 25 = 3X + 2Y
  • Determine the values of X and Y that will maximize utility. (2 points)

In equilibrium: MUX/Px = MUY/Py. Thus, 0.5Y/3 = 0.5X/2, giving Y = 3/2X.

Use the budget line: 25 = 3X + 3X gives X = 4.12 units so Y = 6.25 units.

Question 3: Individual and Market Demand

3a)The current price charged by a local movie theater is $8. The concession stand earns $5 in revenue for each ticket sold. At P1, the theater sells 300 tickets per movie. If the theater raises prices to $9, 270 ticketsare sold. What is theelasticity of demand? What happens to ticket revenue if the theater increases its prices to $9? If the theater wants to maximize the sum of ticket and concession revenue, should they raise their price to $9? (5 points)

The price elasticity of demand at $8 is . Initial ticket revenue is P*Q=$8(300)=$2,400. If prices are raised to $9, revenue = $9(270) = $2,430. Thus, if prices are raised, revenue increases by $30.

At $8, the concession stand will average $1,500 per movie. At $9, the stand will average $1,350. Thus, concession stand revenues fall by $150. If the theater wants to maximize the sum of ticket and concession revenue, they should not raise ticket prices to $9.

3b) Suppose that at a price of $4 per bushel, the quantity supplied of corn is 25 million metric tons. At a price of $6 per bushel, the quantity supplied is 30 million metric tons. Using the arc method, what is the elasticity of supply for corn? Is supply elastic or inelastic (explain your answer)? (2 points)

∆Q/Q = (30 – 25)/(27.5)

∆P/P = (6 – 4)/5

Es =0.182/0.4 = 0.455. Thus, supply is inelastic (<1) which means that firms are not too responsive to changing prices.

3c) The San Francisco Chronicle reported that the toll on the Golden GateBridge was raised from $2 (P1) to $3 (P2). Following the toll increase, traffic fell by 5%. Calculate the point elasticity of demand. The chairman of the bridge’s finance committee warned that this toll increase would cause toll revenues to decrease by $2.8 million per year. Is this statement consistent with economic theory? Explain. (3 points)

Increasing the toll on the bridge from $2 to $3 is a 50% increase. Traffic is expected to decrease by 5% as a result. Thus, the point price elasticity of demand is -5/50 or -0.1. Demand is inelastic, which means that the chairman’s statement is not consistent with economic theory, as an increase in price will increase total toll revenue, not decrease it.

3d) The demand for bread is estimated as Q = 600 – 150P. Graph this demand curve (2 points). If the price were $1, how many loaves of bread would be purchased? What is consumer surplus at this price? (2 points). Suppose that the price doubles. Calculate the loss in consumer surplus. (1 point)

When Q = 0, p = 4; when p = 0; Q = 600. Draw the graph.

If p =$1, Qd = 450 loaves; CS = ½(450)(3) = 675

If P = $2; Qd = 300; CS = ½(300)(2) = 300. Thus, ∆CS = $375

Question 4: Production

4a) Complete the following tableand using a diagram, explain the relationship between the MPL and the APL (4 points):

L / Q / MPL / APL
0 / 0 / ----- / -----
1 / 50 / 50 / 50
2 / 80 / 30 / 40
3 / 90 / 10 / 30
4 / 96 / 6 / 24
5 / 100 / 4 / 20
6 / 96 / -4 / 16

As MPL decreases, it starts pulling down the APL. See Figure 6.2

4b) A bakery operating in the short-run found that when the level of employment in its baking room was increased from 4 to 10 (one extra worker at a time), its total production of bread rose as follows: 110, 115, 122, 127, 130, 132, 133.Calculate the marginal product of labor, and explain whether this production function exhibits diminishing marginal productivity of labor. (3 points)

L / TP / MPL
4 / 110 / -
5 / 115 / 5
6 / 122 / 7
7 / 127 / 5
8 / 130 / 3
9 / 132 / 2
10 / 133 / 1

This production function does exhibit diminishing returns to labor. Labor inputs of 7 or more yield diminishing marginal returns, because the MPL is decreasing in this input range.

4c) You are given the following table for a production process which has two variable inputs.Sketch the isoquants corresponding to the following output levels: 70, 95, and 115. (4 points) What can be said of the MRTS, and what does this imply?(2 points) What returns to scale does this production function exhibit? (2 points)

Labor Input
Capital Investment / 1 / 2 / 3 / 4 / 5
1 / 35 / 60 / 70 / 85 / 95
2 / 60 / 70 / 85 / 95 / 105
3 / 70 / 85 / 95 / 105 / 115
4 / 85 / 95 / 105 / 115 / 125
5 / 95 / 105 / 115 / 125 / 135

Sketch the isoquants with K on vertical, L on horizontal. Given these isoquants are linear, MRTS is constant so K and L are perfect substitutes. Returns to scale can be determined by examining main diagonal. As we move from 1L, 1K to 2L, 2K, output rises from 35 to 70, which implies constant returns to scale. As we move from 2L, 2K to 3L, 3K, input was increased 1½ times, but output rises from 70 to 95 (1.36 proportional increase). From 2L, 2K to 3L, 3K, the production function exhibits decreasing returns to scale, and does so for the remaining input combinations.