ECON 102 Tutorial: Week 6 Shane Murphy

ECON 102 Tutorial: Week 6

Shane Murphywww.lancaster.ac.uk/postgrad/murphys4

http://www.lancaster.ac.uk/postgrad/murphys4

Cost and Production Questions

Key Concepts needed for these questions: Perfectly competitive firms are price takers, so for them MR = P. For all firms, profit is maximized at the quantity where MR = MC.

When we want to understand how a firm makes entry/exit decisions, we use the shutdown conditions – these are different for the short run and the long-run: Short-run shutdown condition:

A firm should shut down when MR < AVC.If the firm is perfectly competitive, this is when P < AVC.This can also be written as when TR < VC.

Long-run shutdown condition:A firm should shut down when MR < ATC.If the firm is perfectly competitive, this is when P < ATC.

This can also be written as when TR < TC or when profit < 0.

Question 1: Ch. 5 Problem 2

A price-taking firm makes air conditioners. The market price of one of their new air conditioners is €120. Its total cost information is given in the table below.Air conditioners

per day

Total cost

(€ per day)

1 100

2 150

3 220

4 310

5 405

6 510

7 650

8 800

How many air conditioners should the firm produce per day if its goal is to maximise its profit?


A price-taking firm makes air conditioners. The market price of one of their new air conditioners is €120. Its total cost information is given in the table below.

Air conditioners

per day

Total cost

(€ per day)

Marginal Cost

(€ per day)

1 100

2 150 50

3 220 70

4 310 90

5 405 95

6 510 105

7 650 140

8 800 150

How many air conditioners should the firm produce per day if its goal is to maximise its profit?

Profit is maximized where MR = MC. Because this firm is a price taker, we know that MR = P. So what we want to find is at what quantity is MC = P?

The MC for each of the first 6 air conditioners produced each day is less than €120 (MC<P), but the marginal cost of the 7th air conditioner is €140, (MC>P).

So the company should produce 6 air conditioners per day.

Number of bats per day

Number of employee-hours per day

0 0 5 110 215 420 725 1130 1635 22

Question 2: Ch. 5 Problem 3(a)The Paducah Slugger Company makes baseball bats out of lumber supplied to it by Acme Sporting Goods, which pays Paducah €10 for each finished bat. Paducah’s only factors of production are lathe operators and a small building with a lathe. The number of bats per day it produces depends on the number of employee-hours per day, as shown in the table below.


Number of employee-hours per day

Total Revenue(€/day)

Total labor cost

(€/day)

Total cost(€/day)

Profit(€/day)

0 0 5 110 215 420 725 1130 1635 22

If the wage is €15 per hour and Paducah’s daily fixed cost for the lathe and building is €60, what is the profit-maximising quantity of bats?

TR = P*Q VC = wage* TC = FC + VC π=TR – TC # of employee hrs.

Question 2: Ch. 5 Problem 3(a)

The Paducah Slugger Company makes baseball bats out of lumber supplied to it by Acme Sporting Goods, which pays Paducah €10 for each finished bat. Paducah’s only factors of production are lathe operators and a small building with a lathe. The number of bats per day it produces depends on the number of employee-hours per day, as shown in the table below.If the wage is €15 per hour and Paducah’s daily fixed cost for the lathe and building is €60, what is the profit-maximising quantity of bats?


Number of employee-

hours per day


Total labor cost

(€/day)

Total cost

(€/day)

Profit(€/

day)

0 0 0 0 60 -60 5 1 50 15 75 -2510 2 100 30 90 1015 4 150 60 120 3020 7 200 105 165 3525 11 250 165 225 2530 16 300 240 300 035 22 350 330 390 -40

As indicated by the entries in the last column of the table to the right, the profit-maximizing quantity of bats for Paducah is 20/day, which yields daily profit of €35.

Question 2: Ch. 5 Problem 3(b)

What would be the profit-maximising number of bats if the firm’s fixed cost were not €60 per day but only €30?

Q (bats/day)

Number of employee-hours per

day


Total labor cost

(€/day)

Total cost

(€/day)

Profit(€/day)

0 0 0 0 30 -305 1 50 15 45 5

10 2 100 30 60 4015 4 150 60 90 6020 7 200 105 135 6525 11 250 165 195 5530 16 300 240 270 3035 22 350 330 360 -10

Same quantity as in part a, but now profit is €65, or €30 more than before.


For the pizza seller whose marginal, average variable and average total cost curves are shown in the diagram below, what is the profit-maximising level of output and how much profit will this producer earn if the price of pizza is €2.50 per slice?



To answer this question, we use the same rule as we did in Ch. 5 Problem 2: For a perfectly competitive firm, profit is maximized where MC = P.

This firm will sell 570 slices per day, the quantity for which P = MC. Its profit will be: π = (P-ATC)*Q π = (€2.50/slice - €1.40/slice)*(570 slices/day) π = €627/day.





This firm will sell 360 slices per day, the quantity for which P = MC. Its profit will be: π = (P-ATC)*Q π = (€0.80/slice - €1.03/slice)*(360 slices/day) π = -€82.80/day.




For the pizza seller whose marginal, average variable and average total cost curves are shown in the diagram below, what is the profit-maximising level of output and how much profit will this producer earn if the price of pizza is €0.50 per slice?Because price is less than the minimum value of AVC, this producer will shut down in the short run. He will experience a loss equal to his fixed cost. Fixed cost is the difference between total cost and total variable cost.

For Q = 260 slices/day, we know both ATC and AVC, so for that output level we can calculate: TC = ATC*Q = (260 slices/day)*(€1.18/slice) = €306.80/day VC = AVC*Q = (260 slices/day)*(€0.68/slice) = €176.80/day. So fixed cost, FC = TC - VC = €306.80/day - €176.80/day = €130/day. This producer’s profit is thus - €130/day.

Question 6The table below gives the relationship between the number of workers in a firm, and the total output that can be produced per day. Workers are paid $20 per day. a) Fill in the rest of the table, expressing each of the costs in the cost per day for the firm. (Note: AFC is average fixed cost, AVC is average variable cost, ATC is average total cost, and MC is marginal cost)

Does this production technology exhibit diminishing marginal products? Explain.

Workers Q Fixed Costs

Variable Costs

Total Cost AFC AVC ATC MC

0 0 10 - - - -

1 25

2 63

3 94

4 119

5 140

6 158




Variable Costs


0 0 10 0 10 - - - -

1 25 10 20 30

2 63 10 40 50

3 94 10 60 70

4 119 10 80 90

5 140 10 100 110

6 158 10 120 130




Variable Costs


0 0 10 0 10 - - - -

1 25 10 20 30 10 20 30 20

2 63 10 40 50 5 20 25 20

3 94 10 60 70 3.33 20 23.33 20

4 119 10 80 90 2.25 20 22.5 20

5 140 10 100 110 2 20 22 20

6 158 10 120 130 1.66 20 21.66 20

Perfect Competition Questions

Question 1: Ch. 7 Problem 3(a)

John Jones owns and manages a café whose annual revenue is €5,000. The annual expenses are as in the table below.Expense €Labour 2,000Food and drink 500Electricity 100Vehicle lease 150Rent 500Interest on loan for equipment 1,000

Calculate John’s annual accounting profit.

John's accounting profit is his revenue minus his explicit costs, or €750 per year.

Question 1: Ch. 7 Problem 3(b)


John could earn €1,000 per year as a recycler of aluminium cans. However, he prefers to run the café. In fact, he would be willing to pay up to €275 per year to run the café rather than to recycle cans. Is the café making an economic profit? Should John stay in the business? Explain.

Yes: his opportunity cost of his labour to run the café is €1,000 - €275, or €725 per year. Adding this implicit cost to the explicit costs implies that the café is making an economic profit of €25 per year. And since €25>0, John should stay in business.

Question 1: Ch. 7 Problem 3(c)


Suppose the café’s revenues and expenses remain the same, but recyclers’ earnings rise to €1,100 per year. Is the café still making an economic profit? Explain.

John's opportunity cost rises by €100, to €825 per year. The café is thus now making an economic loss of €75 per year.

Question 1: Ch. 7 Problem 3(d)


Suppose John had not had to get a €10,000 loan at an annual interest rate of 10 per cent to buy equipment, but instead had invested €10,000 of his own money in equipment. How would your answers to parts (a) and (b) change?

The accounting profit would now be €1,750/yr. The answer to part b. would not change. If John had €10,000 of his own to invest in the café, he would forgo €1,000/yr in interest by not putting the money in a savings account. That amount is an opportunity cost that must be included when calculating economic profit.

Question 1: Ch. 7 Problem 3(e)


If John can earn €1,000 a year as a recycler, and he likes recycling just as well as running the café, how much additional revenue would the café have to collect each year to earn a normal profit?

To earn a normal profit, the café would have to cover all its implicit and explicit costs. The opportunity cost of John's time is €1,000/yr, whereas the café's accounting profit is only €750/yr. Thus, the café would have to earn additional revenues of €250/yr to make a normal profit.

Perfect Competition Q2(a)

Dave owns a firm that produces and sells gizmos in a perfectly competitive market. His fixed costs are $200 per day, and his variable costs are VC(Q) = 2Q2. (given this variable cost curve, Dave’s marginal cost curve is: MC(Q) = 4Q.). Assume that each firm in this market has the same costs as Dave, and the costs I’ve described include both implicit and explicit costs.If the current market price of gizmos is $60, how many gizmos does Dave produce to maximize his profit? How much economic profit does Dave earn?

Perfect Competition Q2(a) Dave owns a firm that produces and sells gizmos in a perfectly competitive market. His fixed costs are $200 per day, and his variable costs are VC(Q) = 2Q2. (given this variable cost curve, Dave’s marginal cost curve is: MC(Q) = 4Q.). Assume that each firm in this market has the same costs as Dave, and the costs I’ve described include both implicit and explicit costs.If the current market price of gizmos is $60, how many gizmos does Dave produce to maximize his profit? How much economic profit does Dave earn?We know that Dave’s marginal cost curve is MC(Q) = 4Q. Because Dave’s firm is in a perfectly competitive market, we know that it maximizes profit when MC(Q) = P. We can re-write this as: 4Q = 60 And solve for Q: Q = 15 To find Dave’s economic profit, we use the equation: π = TR – TC, where TR = P*Q and TC = FC + VC. When Dave produces Q = 15 units, his total variable costs are: VC(Q) = 2Q2 = 2(15)2 = 450 and his fixed costs are FC = 200. We can plug these in to the equation for economic profit: π = TR – TC

π = P*Q – FC - VC π = 15*60 – 200 - 450

π = 900 – 650 π = 250

Perfect Competition Q2(b)

Is the market price of $60 sustainable in the long run? Explain why or why not.

No, this market price is not sustainable in the long run. Since firms in the industry are earning positive economic profit, new entrants will enter the industry; this will shift the supply curve to the right and drive the price down.

Perfect Competition Q2(c)

Dave owns a firm that produces and sells gizmos in a perfectly competitive market. His fixed costs are $200 per day, and his variable costs are VC(Q) = 2Q2. (given this variable cost curve, Dave’s marginal cost curve is: MC(Q) = 4Q.). Assume that each firm in this market has the same costs as Dave, and the costs I’ve described include both implicit and explicit costs.

Write down the expression for Dave’s total costs

The equation for Total Cost is: TC(Q) = FC + VC(Q) So Dave’s Total Cost is: TC(Q) = 200 + 2Q2

Perfect Competition Q2(d)

Dave owns a firm that produces and sells gizmos in a perfectly competitive market. His fixed costs are $200 per day, and his variable costs are VC(Q) = 2Q2. (given this variable cost curve, Dave’s marginal cost curve is: MC(Q) = 4Q.). Assume that each firm in this market has the same costs as Dave, and the costs I’ve described include both implicit and explicit costs.In part (c), we found TC(Q) = 200 + 2Q2

Write down the expression for Dave’s average total cost

Perfect Competition Q2(d)

Dave owns a firm that produces and sells gizmos in a perfectly competitive market. His fixed costs are $200 per day, and his variable costs are VC(Q) = 2Q2. (given this variable cost curve, Dave’s marginal cost curve is: MC(Q) = 4Q.). Assume that each firm in this market has the same costs as Dave, and the costs I’ve described include both implicit and explicit costs.

Write down the expression for Dave’s average total costThe equation for Average Total Cost is:

ATC(Q) = TC(Q)/QPlug in Dave’s total cost from part (c): ATC(Q) = (200 + 2Q2)/QSo Dave’s Average Total Cost is: ATC(Q) = 200/Q + 2Q

Perfect Competition Q2(e)

Solve for the long-run equilibrium price.We know that we have a perfectly competitive market. FC = $200/day, variable costs are VC(Q) = 2Q2 and Dave’s marginal cost curve is: MC(Q) = 4Q.In parts (c) and (d), we found TC = 200 + 2Q2 and ATC = 200/Q + 2Q.

Perfect Competition Q2(e)

Solve for the long-run equilibrium price.The long-run equilibrium price is the price where firms earn zero economic profit. This happens at the minimum of the ATC cost curve. To find the minimum of the ATC curve, recall that when MC = ATC, ATC is at its minimum. So, we can set MC(Q) = ATC(Q). We know that MC(Q) = 4Q, that was given in the problem.In part (d) we found ATC(Q) = 200/Q + 2Q. So let’s set MC(Q) = ATC(Q) Plugging in, we get: 4Q = 200/Q + 2Q

2Q = 200/Q 2Q2 = 200 Q2 = 100 Q = 10

So, ATC(Q) reaches its minimum when Q = 10. To find the value of ATC, we can plug in Q = 10 into ATC(Q) = 200/Q + 2Q.

ATC(Q) = 200/10 + 2(10) = 40 Thus, the long-run equilibrium price is 40.

Exam on Friday

50 minutes; 24 Questions: 16 from Rietzke, 8 from Peel. What to Revise: Practice MC Questions, Tutorial worksheets,

Peel’s Maths Questions, Lecture Notes, and textbook chapters.

Check your timetable for Exam time and location. Bring a pencil and eraser.

No calculators, cell phones, or electronic translators will be allowed. (Paper versions of English-to-Other Language dictionaries will be allowed and checked by invigilators).

Also, for next week, there will be a tutorial worksheet on Moodle.

Good luck and see you next week!

If an indifference curve is smooth and convex to the origin, then:

a) The two goods are said to be convex combinations of each other

b) There is a diminishing marginal rate of substitution

c) The indifference curve is said to be normald) None of the above

Q5

From Tutorial 4 worksheet: Question 1Assuming an indifference curve which is convex to the origin, what can this tell us about a consumer’s marginal rate of substitution between coffee and muffins?

A profit maximizing firm would like to produce at least the number of units which minimises short run:

a) Average total costb) Average fixed costc) Average variable costd) Marginal cost

Note: A profit-maximizing firm produces at the efficient scale: the quantity of output that minimizes ATC. We can find this quantity where MC = ATC. Q18

Long Run Exit Condition

• In the long run, firms will continue if there is a profit, so the exit condition is:

Profit < 0TR – TC < 0TR < TCAR < ATCP < ATC

Short Run Exit Condition

• In the short run, fixed costs are sunk costs and firms will run if there is greater profit from continuing than from exiting. The firm pays the fixed cost whether it continues or exits the market, so the exit condition is:

TR – (VC+FC) < -FCTR-VC-FC < -FCTR – VC < 0TR < VCAR < AVCP < AVC

MC=S

P, C

0 q

AVC

• So a firm’s short run exit condition is P < AVC

• Since a firms supply curve is equal to its Marginal Cost Curve, and since MC = AVC at the minimum of AVC, if Q is less than the quantity that minimizes AVC, P will be less than AVC for that Q.

Suppose demand curve written D=120-2P, and the supply curve is S=20+2P. What is the equilibrium price and quantity?

a) P*=70 and Q*=25b) P*=25 and Q*=70c) P*=50 and Q*=35d) P*=35 and Q*=50

Note: Set the two equations equal to each other and solve for P. Plug that value back in to either equation to solve for Q. Q22

Suppose a product has a demand curve written D = 120 – 2P, and the supply curve is S = 20 + 2P. What is the equilibrium price and quantity.

Equilibrium occurs where D = S, i.e.120 – 2P = 20 + 2P100 = 4PP = 25Then, substitute P = 25 into either the D or S equation:D = 120 – 2 * 25 = 70orS = 20 + 2*25 = 70

a. P* = 70 and Q* = 25b. P* = 25 and Q* = 70c. P* = 50 and Q* = 35d. Q* = 35 and P* = 50

http://www.lums.lancs.ac.uk/

Suppose demand is given by D=120-2P and supply is originally S=20+2P but the government imposes a tax of 10 on this good. What happens to the equilibrium price?

a) Rises by 10b) Rises by 8c) Rises by 5d) Rises, but it’s not possible to say by how much

Q23

We have D=120-2P and S=20+2P Then a tax of 10 is imposed on this good. What happens to the equilibrium price?

There are two ways we can solve this. 1. By assuming that the tax is placed on consumers,

thus affecting the Demand curve (shifting it to the left)

2. By assuming that the tax is placed on suppliers/sellers, thus affecting the Supply curve (shifting it to the left).

I’ll work through both methods in the following slides.

We have D=120-2P and S=20+2P Then a tax of 10 is imposed on this good. By assuming that the tax is placed on consumers, thus affecting the Demand curve (shifting it to the left)The new demand curve can be written as:

D = 120 – 2(P+T), where T = 10.D = 120 – 2P -20D = 100 – 2P

We then need to find where this new demand curve crosses the supply curve.

D = S 100 – 2P = 20 + 2P 80 = 4P P = 20

This gives us the new market equilibrium price. It is the price that the consumers will give to the suppliers for each good purchased. On top of this, the consumers must pay the tax of 10, so the total cost to the consumers will be: P + T = 30. So the actual price consumers pay will rise by $5 because of this tax.

We have D=120-2P and S=20+2P Then a tax of 10 is imposed on this good. By assuming that the tax is placed on suppliers, thus affecting the Supply curve (shifting it to the left)The new Supply curve can be written as:

S = 20 + 2(P-T), where T = 10.S = 200 + 2P -20S = 2P

We then need to find where this new supply curve intersects with our original demand curve.

D = S120 – 2P = 2P120 = 4PP = 30

This gives us the new market equilibrium price. It is the price that the consumers will give to the suppliers for each good purchased. From this, the sellers have to pay the government a tax of 10, so the total cost to the consumers will be: P = 30 and the total amount that sellers receive will be 20. So the actual price consumers pay will rise by $5 because of this tax.

Suppose D=10/P, work out the price elasticity at P=10 and P = 20 and P=30.

a) Not possible to say without knowing what the corresponding level of demand is.

b) -1, -2, -3c) -3, -2, -1d) -1, -1, -1

Q25

Suppose D=10/P, work out the price elasticity at P=10 and P = 20 and P=30.

Because we are asked to find the price elasticity at a specific point, we will use the point elasticity method. The equation for point elasticity is: = Step 1: we can solve for :

D = 10/P = 10

Now that we have dD/dp, we can plug it into our point elasticity equation for any value of P and the corresponding Q. Q25

We have solved for .Step 2: we need to solve for Q when P = 10 by plugging into the demand equation that was given.

D = 10/PD = 10/10 D = 1

Step 3: we can plug all of these parts into the elasticity equation : =

=== = = -1

To find elasticity when P = 20 and P = 30, repeat steps 2&3. Q25

(remember, in equilibrium D = S= Q, so when P = 10, Q = 1))

Suppose supply is perfectly elastic at a price of £10 and the government imposes a tax of £2 on a good whose demand curve is given by D=100-5P. Compute the amount of tax revenue raised, the deadweight loss of the tax, and the change in consumer surplus.

a) 10, 80, 90b) 80, 10, 90c) 10, 90, 100d) 10, 75, 85

Q26

Suppose supply is perfectly elastic at a price of £10 (i.e. the S curve is horizontal) and the government imposes a tax of £2 (so the S curve shifts upward by 5) on a good whose demand curve is given by D = 100 – 5P. Compute the amount of tax revenue raised, the deadweight loss of the tax, and the change in consumer surplus.

P

0 D

20

1210

SS’

P = 20 – 1/5 D

To find horizontal intercept:0 = 20 – 1/5 D1/5 D = 20D = 100

If P = 10, 10 = 20 – 1/5 DD = 50If P = 12,12 = 60 – ½ DD = 40

D

40 50 100


Continued:Compute the amount of tax revenue raised, the deadweight loss of the tax, and the change in consumer surplus.

P

0 D

20

1210 S

S’

D

40 50 100

Tax Revenue:£2 * 40 = 80

DWL:½ * 10 * 2 = 10

CS = ½ * 50 * 10 = 250CS’ = ½ * 40 * 8 = 160CS – CS’ = 90

a) 10, 80, 90b) 80, 10, 90c) 10, 90, 100d) 10, 75, 85

Tax


Suppose the TC curve for a firm where TC=12+4Q+Q2 and MR=8. What level of output will the firm produce in order to maximise profit (ie where MC=MR)?

a) 0b) 2c) 4d) 8

Q30

Suppose the TC curve for a firm where TC = 12 + 4Q + Q^2 and MR = 8. What level of output will the firm produce in order to maximise profit (i.e. where MC = MR)?

Remember the ruleslope of Y = b.Xc is c.b.Xc-1

a. 0b. 2c. 4d. 8

2

42

842

:

8

24

2412 2

Q

Q

Q

MRMC

MR

QMC

QQTC


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ECON 102 Tutorial: Week 6 Shane Murphy