econ 100 tutorial: week 13 office hours: 3:45pm to 4:45pm tuesday lums c85

ECON 100 Tutorial: Week 13

www.lancaster.ac.uk/postgrad/alia10/[email protected]

office hours: 3:45PM to 4:45PM tuesday LUMS C85

Question 1Suppose the inverse demand function is given by P=450-2Q. And the supply curve is given by MPC=30+2Q where MPC is the marginal PRIVATE costs. In addition there are social costs given by MSC=Q – that is every unit of output of the generates $1 of additional costs to society over an above the costs of production. The diagram below illustrates the market.

Question 1(a)Inverse demand function: P=450-2QSupply Curve: MPC=30+2Q , where MPC is the marginal PRIVATE costs. Social costs given by MSC=QWhat is the competitive level of output, Qc, and competitive price, Pc?

To find Q, set the Marginal Private Cost equal to the inverse demand function:30+2Q = MPC = P = 450-2Q30+2Q = 450-2Q4Q = 420Q = 420/4Q = 105

Plug this Q into the demand function:P = 450 – 2 (105)P = 450 – 210P = 240

Ps

Pc

Qs Qc

Question 1(b)Inverse demand function: P=450-2QSupply Curve: MPC=30+2Q , where MPC is the marginal PRIVATE costs. Social costs given by MSC=QWhat is the socially optimal output and price?

We need to find MPC+MSC:MPC+MSC = 30 + 2Q + Q = 30 + 3QSet this equal to demand:30 + 3Q = 450 – 2Q5Q = 420 Q = 84

Plug this into demand:P = 450 – 2(84)P = 450 – 168P = 282

Ps

Pc

Qs Qc

Question 1(c)

Social optimum

Competitive optimum Difference

Consumer surplus A+B+C+DPrivate producer surplus, PSp F+G+HExternality cost C+D+E+G+HSocial producer surplus, PSs F-C-D-ESocial welfare W=CS+PSs A+B+F-E

Complete the following table using the areas labelled in the diagram:

This graph shows a scenario where there is some sort of Marginal social cost due to a production/supply externality.

Qs Qc

Ps

Pc

Question 1(c)Consumer

Surplus

Social optimum


Consumer surplus A+B+C+DPrivate producer surplus, PSpExternality costSocial producer surplus, PSsSocial welfare W=CS+PSs


Question 1(c)Consumer

Surplus

Social optimum


Consumer surplus A A+B+C+D B+C+DPrivate producer surplus, PSpExternality costSocial producer surplus, PSsSocial welfare W=CS+PSs


Question 1(c)Private

Producer Surplus

Social optimum


Consumer surplus A A+B+C+D B+C+DPrivate producer surplus, PSp F+G+HExternality costSocial producer surplus, PSsSocial welfare W=CS+PSs


PsPc

Producer surplus is the area under the price and above the MPC.

Question 1(c)Private

Producer Surplus

Social optimum


Consumer surplus A A+B+C+D B+C+DPrivate producer surplus, PSp B+C+G+F F+G+H H-B-CExternality costSocial producer surplus, PSsSocial welfare W=CS+PSs


Producer surplus is the area under the price and above the MPC.

Question 1(c)Externality

Cost

Social optimum


Consumer surplus A A+B+C+D B+C+DPrivate producer surplus, PSp B+C+G+F F+G+H H-B-CExternality cost C+D+E+G+HSocial producer surplus, PSsSocial welfare W=CS+PSs


Note: The cost of an externality is actually everything under the marginal social cost curve, up to the Q. We show it this way (MSC+MPC) because it makes it easier to find the equilibia.

Question 1(c)Externality

Cost

Social optimum


Consumer surplus A A+B+C+D B+C+DPrivate producer surplus, PSp B+C+G+F F+G+H H-B-CExternality cost C+G C+D+E+G+H D+E+HSocial producer surplus, PSsSocial welfare W=CS+PSs


Note: The cost of an externality is actually everything under the marginal social cost curve, up to the Q. We show it this way (MSC+MPC) because it makes it easier to find the equilibia.

Question 1(c)Social

producer surplus

Social optimum


Consumer surplus A A+B+C+D B+C+DPrivate producer surplus, PSp B+C+G+F F+G+H H-B-CExternality cost C+G C+D+E+G+H D+E+HSocial producer surplus, PSs F-C-D-ESocial welfare W=CS+PSs


Another way of thinking about social producer surplus is PSs = PSp – E

Question 1(c)Social

producer surplus

Qs Qc

PsPc

Another way of thinking about social producer surplus is PSs = PSp – ESo, if we are producing at Qc and the price is Pc, our Producer surplus is areas F+G+H. The Externality cost is G+C+D+H+E. If we subtract one from the other, we get:PSs = F+G+H-G-C-D-H-EPSs = F+G-G+H-H-C-D-EPSs = F-C-D-E

Question 1(c)Social

producer surplus

Social optimum


Consumer surplus A A+B+C+D B+C+DPrivate producer surplus, PSp B+C+G+F F+G+H H-B-CExternality cost C+G C+D+E+G+H D+E+HSocial producer surplus, PSs B+F F-C-D-E -B-C-D-ESocial welfare W=CS+PSs


Another way of thinking about social producer surplus is PSs = PSp – E

Question 1(c)Social welfare

Social optimum


Consumer surplus A A+B+C+D B+C+DPrivate producer surplus, PSp B+C+G+F F+G+H H-B-CExternality cost C+G C+D+E+G+H D+E+HSocial producer surplus, PSs B+F F-C-D-E -B-C-D-ESocial welfare W=CS+PSs A+B+F-E


Another way of thinking about social welfare is W = CS + PS -E

Question 1(c)Social welfare

Social optimum


Consumer surplus A A+B+C+D B+C+DPrivate producer surplus, PSp B+C+G+F F+G+H H-B-CExternality cost C+G C+D+E+G+H D+E+HSocial producer surplus, PSs B+F F-C-D-E -B-C-D-ESocial welfare W=CS+PSs A+B+F A+B+F-E -E


Another way of thinking about social welfare is W = CS + PS -E

Question 2(a)Explain what is meant by excludability and rivalry.

Excludable: A good or service is called excludable if it is possible to prevent individuals who have not paid for it to have access to it.

Rival: A good or service is called rival if it’s consumption by one consumer prevents simultaneous consumption by other consumers.

We use these two characteristics to divide goods into four categories:

Why do we care about these distinctions?How well markets work in providing goods depends on the characteristics of those goods. Markets work best for private goods (which are both rival and excludable). But they do not work as well for other types of goods. In such cases government policy is used to remedy market failure and raise economic well-being.

Excludable Non-excludableRival Private goods Common propertyNon-rival Club good Public good

Question 2(a)Give two examples of rival, non-rival, excludable, and non-excludable goods.

Excludable: A good or service is called excludable if it is possible to prevent individuals who have not paid for it to have access to it.

Rival: A good or service is called rival if it’s consumption by one consumer prevents simultaneous consumption by other consumers.

Excludable Non-excludableRival Private goods:

food, clothing, cars

Common property: fish stocks, timber, coal

Non-rival Club goods: cinema, private park, satellite telly

Public goods: Free-to-air radio/ television, air, national defence

Question 2(b)Security guards protect the two tenants of a shopping mall (it's a US story). Guards cost a wage of W=$10 per hour. Store 1 with Demand D1 , such that W=18-2G, is willing to hire 4 guards an hour (it's a big-box store). The market for guards is competitive and will supply as much as required at $10 an hour. Store 2, with Demand D2, such that W=7-G, and so is not willing to hire any guards (it's a small boutique) at the going wage.

The services that a guard provides is a public good - so the boutique can benefit from whatever the big-box store hires. The social demand is the vertical sum of the demand curves for the two stores. Draw a diagram to capture this problem. Show what the social and the competitive private optima are.

Question 2(b)Guards wage: W=$10 per hour. The market for guards is competitive and will supply as much as required at $10 an hour.That gives us our supply curve. Horizontal at MC = 10.

Then we can re-arrange the following two demand curves into Y = mX + c form:Store 1’s Demand D1 , such that W=18-2G, is willing to hire 4 guards an hour. Store 2’s Demand D2, such that W=7-G, is willing to hire 0 guards an hour. This is what we have so far:

Next, we’ll graph the Social Demand curve so that we can Find the social optimum.

Question 2(b)Guards wage: W=$10 per hour. The market for guards is competitive and will supply as much as required at $10 an hour. Store 1’s Demand D1 , such that W=18-2G, is willing to hire 4 guards an hour. Store 2’s Demand D2, such that W=7-G, is willing to hire 0 guards an hour.

The services that a guard provides is a public good. The social demand is the vertical sum of the demand curves for the two stores.

Draw a diagram to capture this problem. What is the social optimum?

G* = 5What is the competitive private optimum?

Gc = 4

Note: If 5 guards are hired, store 1’s demand implies it is willing to pay 18 – 2(5) = $8 and store 2 is willing to pay 7-5 = $2

Question 3(a)Suppose the demand for oil is Qt = 200 – Pt in each year, t=1,2. All the oil is extracted and sold by the end of the two periods. Suppose the marginal cost of extraction is zero. Show how the price of oil at time t depends on the interest rate, i, and on the total supply of oil. Total supply is given by:

Q = Q1+Q2

Q = (200 – P1) +(200 – P2)The Hotelling Rule says P2 = P1 (1+i). So Pt = (400 – Q)/(2 + i)

Here’s how to get there: Q = (200 – P1) +(200 – P1 (1+i))Q = 400 – P1 – P1 (1+i)Q = 400 – (P1 + P1 (1+i))Q = 400 – P1 (1+1+i)Q = 400 – P1 (2+i)

Q – 400 = -P1 (2+i) 400 – Q = P1 (2+i)

(400 – Q)/(2+i) = P1

Question 3(b)Show that the lower is i the more oil is conserved until year 2.

Ian’s Answer: Since P2 = P1 (1+i), It follows that at a higher i the difference in prices across time will be larger. So with high i P2 will be large relative to P1. Consumers react to this bigger price differential by buying more in period 1 and leaving less for period 2.

Exam 2 notes:Tutors have to turn in marked exams on Feb. 10th, so you’ll receive your marks sometime soon after that date.You will not receive back your exam answer booklet.

Here’s a rough guide to tutorial material that corresponds with the exam questions (in case you’re planning on studying for the final or want to compare it to what you answered):

Q1: Tutorial 10 Question 1Q2: Tutorial 11 Question 2Q3: Tutorial 9 Question 2, and Lecture 20, slide 4 (+ or – a few slides)Q4: Tutorial 12 Question 1, and Lecture 31/32 Slide 22 (+ or – a few slides)Q5: Tutorial 12 Question 3

Next week: Macroeconomics – check Moodle for a worksheet and read through Chapter 23 of Mankiw & Taylor.

econ 100 tutorial: week 13 office hours: 3:45pm to 4:45pm tuesday lums c85

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