. Eye-de-ho Potatoes is a product of the Coeur d=Alene Growers= Association. Producers in the area are able to switch back and forth between potato and wheat production depending on market conditions. Similarly, consumers tend to regard potatoes and wheat (bread and bakery products) as substitutes. As a result, the demand and supply of Eye-de-ho Potatoes are highly sensitive to changes in both potato and wheat prices. Demand and supply functions for Eye-de-ho Potatoes are as follows: QD=-1,450 – 25P + 12. 5PW + 0. 2Y,(Demand) QS=-100 + 75P – 25PW – 12. 5PL + 10R,(Supply) here P is the average wholesale price of Eye-de-ho Potatoes ($ per bushel), PW is the average wholesale price of wheat ($ per bushel), Y is income (GNP in $ billions), PL is the average price of unskilled labor ($ per hour), and R is the average annual rainfall (in inches). Both QD and QS are in millions of bushels of potatoes. A. When quantity is expressed as a function of price, what are the Eye de ho Potatoes demand and supply curves if PW = $4, Y = $7,500 billion, PL = $8, and R = 20 inches? B. Calculate the surplus or shortage of Eye-de-ho Potatoes when P = $1. 50, $2, and $2. 50. C.
Calculate the market equilibrium price/output combination. P3. 1SOLUTION A. When quantity is expressed as a function of price, the demand curve for Eye de ho Potatoes is: QD=-1,450 – 25P + 12. 5PW + 0. 2Y =-1,450 – 25P + 12. 5($4) + 0. 2($7,500) QD=100 – 25P When quantity is expressed as a function of price, the supply curve for Eye de ho Potatoes is: QS=-100 + 75P – 25PW – 12. 5PL + 10R =-100 + 75P – 25($4) – 12. 5($8) + 10(20) QS=-100 + 75P B. The surplus or shortage can be calculated at each price level: Price Quantity Supplied Quantity Demanded Surplus (+) or Shortage (-) (1) (2) (3) (4) = (2) – (3) 1. 50: QS = -100 + 75($1. 50) = 12. 5 QD = 100 – 25($1. 50) = 62. 5 -50 $2. 00: QS = -100 + 75($2) = 50 QD = 100 – 25($2) = 50 0 $2. 50: QS = -100 + 75($2. 50) = 87. 5 QD = 100 – 25($2. 50) = 37. 5 +50 C. The equilibrium price is found by setting the quantity demanded equal to the quantity supplied and solving for P: QD=QS 100 – 25P=-100 + 75P 100P=200 P=$2 To solve for Q, set: Demand: QD = 100 – 25($2)=50 (million bushels) Supply: QS = -100 + 75($2)=50 (million bushels) In equilibrium QD = QS=50 (million bushels). P3. 2 Demand and Supply Curves. Demand and supply conditions in the market or unskilled labor are important concerns to business and government decision makers. Consider the case of a federally mandated minimum wage set above the equilibrium, or market clearing, wage level. Some of the following factors have the potential to influence the demand or quantity demanded of unskilled labor. Influences on the supply or quantity supplied may also result. Holding all else equal, describe these influences as increasing or decreasing, and indicate the direction of the resulting movement along or shift in the relevant curve(s). A. An increase in the quality of secondary education. B.
A rise in welfare benefits. C. An increase in the popularity of self-service gas stations, car washes, and so on. D. A fall in interest rates. E. An increase in the minimum wage. P3. 2SOLUTION A. An increase in the quality of secondary education has the effect of increasing worker productivity and will cause an increase or rightward shift in the demand for unskilled labor. To the extent that the benefits of an increase in the quality of education are recognized by students, more will stay in school and a secondary effect of a decrease or leftward shift in the supply of unskilled labor will also be observed.
This shift will be reinforced as workers Agraduate@ from the unskilled to the skilled segment of the labor force. B. A rise in welfare benefits makes not working more attractive and will cause a decrease or leftward shift in the supply of unskilled labor. C. A Self-service@ gas stations, car washes, and so on, involve a substitution of the consumers own labor for hired unskilled labor. As self-serve increases in popularity, a decrease, or leftward shift, in the demand for unskilled labor occurs. D. Holding all else equal, a fall in interest rates will increase the attractiveness of capital relative to labor.
Employers can be expected to substitute capital for the now relatively more expensive labor. A decrease or leftward shift in the demand for unskilled labor will result. Of course, this influence can be mitigated to the extent that lower interest rates spur capital investment and a subsequent increase in employment opportunities. E. An increase in the minimum wage will have the effect of decreasing the quantity demanded of unskilled labor, while at the same time increasing the quantity supplied. The first involves an upward movement along the demand curve, while the second involves an upward movement along the supply curve.
P3. 3 Supply Curve Determination. Olympia Natural Resources, Inc. , and Yakima Lumber, Ltd. , supply cut logs (raw lumber) to lumber and paper mills located in the Cascades Mountain region in the state of Washington. Each company has a different marginal cost of production depending on its own cost of landowner access, labor and other cutting costs, the distance cut logs must be shipped, and so on. The marginal cost of producing one unit of output, measured as one thousand board feet of lumber (where one board foot is one square foot of lumber, one inch thick), is:
MCO=$350 + $0. 00005QO(Olympia). MCY=$150 + $0. 0002QY(Yakima). The wholesale market for cut logs is vigorously price competitive, and neither firm is able to charge a premium for its products. Thus, P = MR in this market. A. Determine the supply curve for each firm. Express price as a function of quantity and quantity as a function of price. (Hint: Set P = MR = MC to find each firm=s supply curve. ) B. Calculate the quantity supplied by each firm at prices of $325, $350, and $375. What is the minimum price necessary for each individual firm to supply output? C.
Assuming these two firms make up the entire industry in the local area, determine the industry supply curve when P < $350. D. Determine the industry supply curve when P > $350. To check your answer, calculate quantity at an industry price of $375 and compare your result with part B. SOLUTION A. Each company will supply output to the point where MR = MC. Because P = MR in this market, the supply curve for each firm can be written with price as a function of quantity as: Olympia MRO=MCO P=$350 + $0. 00005QO Yakima MRY=MCY P=$150 + $0. 0002QY When quantity is expressed as a function of price:
Olympia P=$350 + $0. 00005QO 0. 00005QO=-350 + P QO=-7,000,000 + 20,000P Yakima P=$150 + $0. 0002QY 0. 0002QY=-150 + P QY=-750,000 + 5,000P B. The quantity supplied at each respective price is: Olympia P=$325: QO = -7,000,000 + 20,000($325) = -500,000 ? 0 (because Q < 0 is impossible) P=$350: QO = -7,000,000 + 20,000($350) = 0 P=$375: QO = -7,000,000 + 20,000($375) = 500,000 Yakima P=$325: QY = -750,000 + 5,000($325) = 875,000 P=$350: QY = -750,000 + 5,000($350) = 1,000,000 P=$375: QY = -750,000 + 5,000($375) = 1,125,000 For Olympia, MC = $350 when Q0 = 0.
Because marginal cost rises with output, Olympia will never supply output unless a price in excess of $350 per unit can be obtained. Because negative output is not feasible, Olympia will simply fail to supply output when P < $350. Similarly, MCY = $150 when QY = 0. Thus, Yakima will never supply output unless a price in excess of $150 per unit can be obtained. C. When P < $350, only Yakima can profitably supply output. The Yakima supply curve will be the industry curve when P < $350: P=$150 + $0. 0002Q or Q=-750,000 + 5,000P D. When P > $350, both Olympia and Yakima can profitably supply output.
To derive the industry supply curve in this circumstance, simply sum the quantities supplied by each firm: Q=QO + QY = 7,000,000 + 20,000P + (-750,000 + 5,000P) =-7,750,000 + 25,000P To check, at P = $375: Q=-7,750,000 + 25,000($375) =1,625,000 which is supported by the answer to part B, because QO + QY = 500,000 + 1,125,000 = 1,625,000 (Note: Some students mistakenly add prices rather than quantities in an attempt to derive the industry supply curve. To avoid this problem, it is important to emphasize that industry supply curves are found through adding up output (horizontal summation), not by adding up prices (vertical summation). P3. 4 Demand Function. The Creative Publishing Company (CPC) is a coupon book publisher with markets in several southeastern states. CPC coupon books are either sold directly to the public, sold through religious and other charitable organizations, or given away as promotional items. Operating experience during the past year suggests the following demand function for CPC=s coupon books: Q = 5,000 – 4,000P + 0. 02Pop + 0. 375I + 1. 5A, where Q is quantity, P is price ($), Pop is population, I is disposable income per household ($), and A is advertising expenditures ($).
A. Determine the demand faced by CPC in a typical market in which P = $10, Pop = 1,000,000 persons, I = $40,000, and A = $10,000. B. Calculate the level of demand if CPC increases annual advertising expenditures from $10,000 to $15,000. C. Calculate the demand curves faced by CPC in parts A and B. P3. 4SOLUTION A. The demand faced by CPC in a typical market in which P = $10, Pop = 1,000,000 persons, I = $40,000, and A = $10,000 is: Q=5,000 – 4,000P + 0. 02Pop + 0. 375I + 1. 5A =5,000 – 4,000(10) + 0. 02(1,000,000) + 0. 375(40,000) + 1. 5(10,000)
