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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
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
Question 1(c)
Social optimum
Competitive optimum Difference
Consumer surplusPrivate producer surplus, PSpExternality costSocial producer surplus, PSsSocial welfare W=CS+PSs
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
Competitive optimum Difference
Consumer surplus A A+B+C+D B+C+DPrivate producer surplus, PSpExternality costSocial producer surplus, PSsSocial welfare W=CS+PSs
Complete the following table using the areas labelled in the diagram:
Qs Qc
Ps
Pc
Question 1(c)Private
Producer Surplus
Social optimum
Competitive optimum Difference
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
Complete the following table using the areas labelled in the diagram:
Qs Qc
Ps
Pc
Question 1(c)Externality
Cost
Social optimum
Competitive optimum Difference
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
Complete the following table using the areas labelled in the diagram:
Qs Qc
Ps
Pc
Question 1(c)Social
producer surplus
Social optimum
Competitive optimum Difference
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
Complete the following table using the areas labelled in the diagram:
Qs Qc
Ps
Pc
PSs = PSp -E
Question 1(c)Social welfare
Social optimum
Competitive optimum Difference
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
Complete the following table using the areas labelled in the diagram:
Qs Qc
Ps
PcAnother way of showing social welfare = CS + PSp -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.
Goods can be categorised by these criteria such that:
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
= (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
P2 = P1 (1+i) = (400 – Q)(1+i)/(2+i)
Question 3(b)Show that the lower is i the more oil is conserved until year 2. If I is close to 1, P2 is nearly double P1, Since Qt = 200 – Pt, this means Q1 will be larger than Q2
If i =0, since P2 = P1 (1+i), P2 = P1,
So Q1 = Q2
Q1 + Q2 is constant, the lower i the higher Q2.
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
