Class Summary | Assignments | Sample Tests | Announcements
1/8: Introduction and coverage of Ch.1; Math review of functional relationships and calculus
1/15: Completed Ch. 2 with emphasis on application involving marginal analysis; Began Ch. 3; Handout and discussion of advertsing problem
1/22: Completed Ch. 2 problems; covered up to price discrimination (p. 101) in Ch. 3
1/29: Completed optimal pricing and price discrimination in Ch. 3; covered up to returns to scale (p. 208) in Ch. 6.
2/5: Review for test, Test 1
2/12: Review tests; completed; Ch 6; began Ch. 7 through definition of short-run cost function (assignments for Ch. 7 shown below)
2/19: Finished Ch. 7.
3/5: Reviewed Chap 7 problems; Completed Ch. 10 (assignments below);
3/12: Reviewed Ch. 10 problems (on Web page); completed Ch. 11
3/19: Will handle any requests on material, chapter problems or sample test; Test 2
3/26: Reviewed Test 2; Finished Ch. 11; Ch. 12 to p. 453
4/2: Plan to finish 12 and 13 (assignments below)
4/9: Finished Chs. 13 and 8;14 (to p. 543)
4/16: Finished Ch. 14; discussed final, handled questions
TEST 1 ANSWERS
1a. TR=75Q-O.O5Q2, MR=75-0.1Q
b. Q=750, P=37.5 (set MR=0)
d. Set P =TR-TC=0 and solve the quadratic: Q=0 or 487
e. Q=243.3, P=62.8 (set MR=MC)
f. P =8833
g. The 2nd derivative of the profit function<0
h. The firm will sell to everyone willing to pay a price of 50 or higher. At P=50, Q=500. Thus the triangular area under the demand curve and above a price of 50=(0.5)(500)(75-50)=6250.
2a. Q=177,000, TR=619,500
b. EP=-0.16, EPo=-0.11.
c. Raise P, must be in elastic portion of demand.
d. Arc EP=-0.2
3a. MRPL=Price times MPL=100/L0.5
b. Set MRPL=PL. L=6.25,Q=50.
4a. Find MP's and show that they decrease as S's increases.
b. Set MPA=MPB and also SA+SB=30. Thus SA=13.33,SB=16.67.
c. Using formula for optimal price, P=20,000 assuming EP remains at -5.
5a. -7.5%, b. 12%, c. 13.3%
TEST 2 ANSWERS
1a. Set MRTSLK==PLPK and solve for L=0.6K
b. TC=1000=40L+20K, Substitute for L=0.6K. Thus K=22.7, L=13.7 and Q=114
2a. AFC=1000/Q, AVC=50-4Q+0.2Q2, SAC=1000/Q+50-4Q+0.2Q2, MC=50-8Q+0.6Q2
b. Set the derivative of AVC=0, Q=10
c. At Q=10, AVC=30
d. The AVC and MC are U-shaped; the supply curve is the MC above the minimum point of the AVC
3a. Set P=MC, Q=15
b. TR-TC=250
c. Set the derivative of LAC=0, Q=10 and LAC=P=80
4a. MR=MCÞ Q=950 and P=310
b. TR-TC=180,500
c. Pc=MC=120 and Qc=1900. Efficiency loss=0.5(950-120)(1900-950)=90,250
5a. Set Qd=QsÞ Q=112 and P=22
b. With P=22, firs are losing money. Some firms will exit reducing supply and raising price until it hits $27.
c. The supply curve shifts up by $5. The price paid by buyers increases (<5) and the net price received by sellers is reduced below 22. Quantity decreases.
6a. Set MR=LMCÞ Q=21 and P=46
b. Set P=LAC. This yields a quadratic with 2 solutions for Q (0 and 41.7). Select the higher output and P=4.6.
ASSIGNMENTS
Core coverage (continued)
Chapter 7: A key chapter on costs that extends the material in Ch. 6. Probs 1-9,11-13,15.
Chapter 10: Perfect competition--the first of three important chapters on market structure. Probs 1-10
Chapter 11: Pure monopoly including cartels, natural monopoly and monopolistic competition: Probs 1-12
Chapter 12: Oligopolies including several models of behavior; a little bit on other dimensions of competition:
Probs 2-6
Chapter 13: Game theory to p. 492: Probs 3-8
Chapter 8: Decision-making under uncertainty, pp. 283-293 and 300-310 (Probs. 2-6,8)
Chapter 14: Regulation, public goods & benefit-cost to p. 552: (Probs. 2.3,8,12)
DUE DATES and PRESENTATIONS
1/29, Ch. 2: Sp-Z (Paul Sp, Barbara W, Larry S on 2/5)
2/5, Ch. 3: M-So (Andrew M, John R, David S on 2/12)
2/12, Ch. 3 or 6: H-L (Greg H, Doyle L on 2/19)
2/19: Ch. 6 or 7: C-G (Denyes K, Tricia G on 2/19)
3/5: Ch. 7 or 10: A-B (John A, Lisa B, Edward B)
3/12: Ch. 10: Sp-Z (Catherine W, John W)
3/19: Test 2 (no presentations)
3/26: Ch. 11: M-So (Mark N, Becky S)
4/2: Ch. 11/12: H-L (Ken H, Tim L)
4/9: Ch. 12/13: C-G (Tim C, Andrew D)
4/16: Ch. 13/8: A-B (Craig A, John A)
Optional Permission: I authorize M. Stano to publish my work, in its original or edited form, for nonprofit, educational purposes. (Sign/Date/telephone number)
STUDENTS' PROBLEMS
Chapter 2
Chapter 3
Chapter 6
Chapter 7
Chapter 10
Chapter 11
Chapter 12
SAMPLE TEST 1 (From Winter 1996)
Value: 60 points--30% of grade. All work must be shown to receive credit.
1. Quopy Quat specializes in printing business cards and resumes using the latest laser technology. The manager estimates weekly demand and cost as:
Q = 25,000 - 1000P and TC = 5,000 + 13Q + 0.002Q2.
a. Determine the firm's revenue maximizing price and output. (3)
b. Determine the profit function and marginal profit function. (2)
c. Determine the profit-maximizing price, output and profit level. (4)
d. Determine the price elasticity of demand at the optimal price. (2)
e. A former employee decides to sue, alleging discrimination. Management agrees to settle out of court by paying the former employee $10,000 a month for the next year. Explain what, if any, impact will this settlement have on Quopy Quat's price and output? (2)
2. Night Timers, a small company manufacturing glow-in-the-dark products, has developed an adhesive tape that can be applied to walls and floors. The total annual cost function is TC = 50,000 + 0.25Q where Q is rolls per year.
a. If management is considering a price of $0.65 per roll, determine the break-even quantity. (2)
b. Suppose that annual demand is estimated as Q = 350,000 - 200,000P. Determine the optimal price and quantity. (4)
c. If capacity is 140,000 rolls per year, what price should the firm set? (2)
d. If the firm can be a perfect price discriminator (ignore the capacity limit), determine the maximum profit potential. (2)
3. Nearby College estimates the demand for its MBA program as:
Q = 5,000 - 0.5P + 0.1Y + 0.2Pc
where Q is the number of students, P is tuition, Y is national GDP in billions, and Pc is the tuition charged by a competitor a few miles away.
a. Determine enrollment if P = $4000, Y = $5000, Pc = $6000. (2)
b. Determine the price elasticity of demand and the cross-price elasticity of demand. (4)
c. What advice do you have for Nearby's administrators. (2)
4. Big State charges instate students $2000 a term and outstate students $4500 a term. The respective demands are:
QI = 25,000 - 3PI and QO = 20,000 - 1.5PO.
a. If the marginal cost per student is $3000, determine Big State's optimal tuition structure (assuming no capacity limits). (4)
b. How will your answer change if Big State's capacity is 10,000 students? (3)
5. Q = 5K0.5L0.5
a. Explain whether the production function has increasing, decreasing or constant returns to scale. (2)
b. Fill in the following table assuming that K = 16. (3)
L Q APL MPL
1 ___ ___ ___
2 ___ ___ ___
3 ___ ___ ___
c. Determine the equations for the marginal product of labor and average product of labor. (3)
d. Explain whether the production function is consistent with the Law of Diminishing Returns to labor. (2)
e. If capital (machines) is fixed at 16, but labor can be varied, determine the optimal amounts of labor if labor costs $10 per unit the price of the good is $25. (3)
f. Find MRTSLK when L = 2 and K = 16. (3)
6. Suppose that a firm's price elasticity of demand is -1.5 and its income elasticity is 2.
a. Explain what will happen to the firm's revenues if it raises its price? (2)
b. If unit cost is constant at $20, determine the optimal price. (2)
c. If incomes are expected to rise by 5%, determine the impact on quantity demanded. (2)
Answers
1 a. Q = 12,500; P =12.5
b. Profit = -5,000 + 12Q -0.003Q*2; Marg Profit + 12 - 0.006Q
c. Q = 2,000, P = 23, Profit = 7,000
d. Ep = -11.5
e. None--doesn't affect MC or MR, profit reduced by 10,000/month (2,500/week)
2a. QB = 125,000
b. Q=150,000, P = 1
c. Q=140,000, P=1.05
d. Maximum profit = 225,000 (i.e., triangular area above P=0.25)
3a. Q=4,700
b. Ep = -0.43; Epo = 0.26
c. raise P (currently in inelastic portion)
4a. QI=7996, PI=5670; Qo=7752,Po=8162
b. Set MRI=MRo and QI+Qo=10,000. Thus QI=4167,PI=6945; Qo=5833,Po=9442
5a. Constant
b. Q: 20, 28.3,34.6;AP:20,14.2,11.5; MP:--,8.3,6.3; MP (calculus):10,7.1,5.8
c. AP=20/L^0.5; MP=10/L^0.5
d. Yes--MP diminishes
e. Need MRPL=PL. Thus L=625
f. (not responsible for this test)
6a. Decreases
b. P = 60
c. 10%
More Detailed ANSWERS - Updated Feb. 2 in Word 6.0 format
SAMPLE TEST 2 (from Winter 1996)
Value: 60 points--30% of grade. All work must be shown to receive credit.
1. Given Q = 10L0.75K0.25, PL = 40, PK = 20.
a. Determine the MRTSLK and the optimal input mix. (4)
b. What is the minimum cost of producing 100 units of output. (5)
c. Determine whether the firm will have economies or diseconomies of scale and sketch the shape of its LAC. Label the axes. (3)
2. A competitive firms's short-run total cost function is:
STC = 25 + 50Q + 10Q2.
a. Determine the equation for AVC and the shut-down price ( A sketch may be helpful). (4)
b. If the market price is 75, how much will the firm produce? (3)
c. Determine the firm's supply function. (3)
3. The long-run average cost for a typical firm in a competitive industry is: LAC = 2500 -4Q + 0.002Q2.
a. What is the long-run price? (3)
b. Explain what will happen if P = 415. (4)
c. If the total level of output in the industry is 72,000 units at the long-run price, how many firms will there be in the industry. (3)
4. A perfectly competitive market has the following demand and supply equations: QD = 60 - 2P and QS = 5P - 10
A typical firm has the short-run total cost function:
STC = 16 + Q2 + 2Q.
a. Determine the equilibrium market price and quantity. (3)
b. Determine the typical firm's output and profits. (4)
c. Suppose a $2 tax is placed on the item. Determine the new price and quantity (A sketch may be helpful). (4)
5. The demand equation for a monopolist is : P = 10,000 - 5Q, Marginal cost is 2,000.
a. Determine the monopolist's profit maximizing price and quantity. (3)
b. Suppose that a 25% tax is levied on the monopoly profits. How will this affect its price and output? (3)
c. Assume that a competitive industry will also be able to provide this commodity at $2,000 per unit. Determine the competitive price and quantity. What is the efficiency (welfare) loss associated with the monopoly (a sketch may be helpful). (4)
6. The movie market for a monopolistically competitive theater has the following daily demand and cost functions:
P = 9 - 0.002Q
LAC = 7 - .004Q + 0.000001Q2.
a. The theater is currently charging $5 a ticket. Is it maximizing profits? (3)
b. Determine the long-run equilibrium price for the industry assuming that demand shifts in a parallel way as a result of entry or exit. (4)
ANSWERS
1a. MRTSLK=3K/L; L=1.5K (by setting 3K/L=PL/PK=2)
b. TC=588 (Set Q=100=10L0.75K0.25 and substitute the optimal mix (L=1.5K). Solve for K and L (7.35 and 11.03) and substitute into isocost equation.
2a. AVC=50+10Q; Shut-down price = 50.
b. Q=1.25 (set P=MC)
c. Q=-2.5+0.05P for al P50
3a. LAC=500 (set dLAC/dQ=0 and solve)
b. Since P<LACmin, there will be exit, a decrease in supply, rising prices until P=500 is attained.
c. N=72,000/1000=72
4a. P=10, Q=40
b. Q=4 (set P=MC), P =0
c. The supply curve shifts up by $2. Thus Qs'=5P-20. Set Qs'=QD and solve (P=11.4,Q=37.2)
5a. Q=800,P=6,000 (set MR=MC)
b. None. No affect on MC or MR.
c. Pc=2,000 (the unit cost), thus Qc=1,600. A monopoly will set MC (2000)=MR. Thus Qm=800 and Pm=6000. The welfare loss triangle is 1,600,000.