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ECON 100 Tutorial: Week 13

ECON 100 Tutorial: Week 13. www.lancaster.ac.uk/postgrad/murphys4/ s.murphy5@lancaster.ac.uk office: LUMS C85. Question 1.

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ECON 100 Tutorial: Week 13

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  1. ECON 100 Tutorial: Week 13 www.lancaster.ac.uk/postgrad/murphys4/ s.murphy5@lancaster.ac.uk office: LUMS C85

  2. Question 1 Suppose 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.

  3. Question 1(a) Inverse demand function: P=450-2Q Supply Curve: MPC=30+2Q , where MPC is the marginal PRIVATE costs. Social costs given by MSC=Q What 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 = 450-2Q 30+2Q = 450-2Q 4Q = 420 Q = 420/4 Q = 105 Plug this Q into the demand function: P = 450 – 2 (105) P = 450 – 210 P = 240

  4. Question 1(b) • Inverse demand function: P=450-2Q • Supply Curve: MPC=30+2Q , where MPC is the marginal PRIVATE costs. • Social costs given by MSC=Q • What is the socially optimal output and price? • We need to find MPC+MSC: • MPC+MSC = 30 + 2Q + Q • = 30 + 3Q • Set this equal to demand: • 30 + 3Q = 450 – 2Q • 5Q = 420 • Q = 84 • Plug this into demand: • P = 450 – 2(84) • P = 450 – 168 • P = 282

  5. Complete the following table using the areas labelled in the diagram: Question 1(c) This graph shows a scenario where there is some sort of Marginal social cost due to a production/supply externality. Ps Pc Qs Qc

  6. Complete the following table using the areas labelled in the diagram: Question 1(c) Consumer Surplus Ps Pc Qs Qc

  7. Complete the following table using the areas labelled in the diagram: Question 1(c) Private Producer Surplus Ps Pc Qs Qc

  8. Complete the following table using the areas labelled in the diagram: Question 1(c) Externality Cost Ps Pc Qs Qc

  9. Complete the following table using the areas labelled in the diagram: Question 1(c) Social producer surplus Ps Pc PSs = PSp -E Qs Qc

  10. Complete the following table using the areas labelled in the diagram: Question 1(c) Social welfare Ps Pc Another way of showing social welfare = CS + PSp -E Qs Qc

  11. 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:

  12. 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.

  13. 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.

  14. 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.

  15. 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* = 5 What 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

  16. 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)

  17. Question 3(b) • Show that the lower isithe more oil is conserved until year 2. • If I is close to 1, P2is 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.

  18. 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 1 Q2: Tutorial 11 Question 2 Q3: 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

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