ECON 100 Tutorial: Week 13 office: LUMS C85

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.

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, Q c, and competitive price, P c ? 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

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 = Q + Q = Q Set this equal to demand: Q = 450 – 2Q 5Q = 420 Q = 84 Plug this into demand: P = 450 – 2(84) P = 450 – 168 P = 282

Question 1(c) Social optimum Competitive optimumDifference Consumer surplus Private producer surplus, PSp Externality cost Social producer surplus, PSs Social 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 optimumDifference Consumer surplusAA+B+C+DB+C+D Private producer surplus, PSp Externality cost Social producer surplus, PSs Social 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 optimumDifference Consumer surplusAA+B+C+DB+C+D Private producer surplus, PSpB+C+G+FF+G+HH-B-C Externality cost Social producer surplus, PSs Social 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 optimumDifference Consumer surplusAA+B+C+DB+C+D Private producer surplus, PSpB+C+G+FF+G+HH-B-C Externality costC+GC+D+E+G+HD+E+H Social producer surplus, PSs Social 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 optimumDifference Consumer surplusAA+B+C+DB+C+D Private producer surplus, PSpB+C+G+FF+G+HH-B-C Externality costC+GC+D+E+G+HD+E+H Social producer surplus, PSsB+FF-C-D-E-B-C-D-E Social 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 optimumDifference Consumer surplusAA+B+C+DB+C+D Private producer surplus, PSpB+C+G+FF+G+HH-B-C Externality costC+GC+D+E+G+HD+E+H Social producer surplus, PSsB+FF-C-D-E-B-C-D-E Social welfare W=CS+PSsA+B+FA+B+F-E-E Complete the following table using the areas labelled in the diagram: Qs Qc Ps Pc Another 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: ExcludableNon-excludable RivalPrivate goodsCommon property Non-rivalClub goodPublic 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. ExcludableNon-excludable Rival Private goods: food, clothing, cars Common property: fish stocks, timber, coal Non-rivalClub 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 D 1, 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 D 2, 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 D 1, such that W=18-2G, is willing to hire 4 guards an hour. Store 2’s Demand D 2, 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 D 1, such that W=18-2G, is willing to hire 4 guards an hour. Store 2’s Demand D 2, 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? G c = 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 Q t = 200 – P t 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 = Q 1 +Q 2 = (200 – P 1 ) +(200 – P 2 ) The Hotelling Rule says P 2 = P 1 (1+i) so P t = (400 – Q)/(2 + i) Here’s how to get there:Q = (200 – P 1 ) +(200 – P 1 (1+i)) Q = 400 – P 1 – P 1 (1+i) Q = 400 – (P 1 + P 1 (1+i)) Q = 400 – P 1 (1+1+i) Q = 400 – P 1 (2+i) Q – 400 = -P 1 (2+i) 400 – Q = P 1 (2+i) (400 – Q)/(2+i) = P 1 P 2 = P 1 (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, P 2 is nearly double P 1, Since Q t = 200 – P t, this means Q 1 will be larger than Q 2 If i =0, since P 2 = P 1 (1+i), P 2 = P 1, So Q 1 = Q 2 Q 1 + Q 2 is constant, the lower i the higher Q 2.

Exam 2 notes: Tutors have to turn in marked exams on Feb. 10 th, 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