Question

Question 1: Suppose the Australian market for uranium ore concentrate is characterized as follows: Market Supply: Q = 0.5P − 40 and Market Demand: Q = 50 − 0.1P, where P is measured in Australian dollars per kiloton of uranium ore concentrate and Q is measured in kilotons of uranium ore concentrate per day. Using this information, answer the following questions.

Part (b) Suppose that after thorough analysis of the Australian market for uranium ore concentrate, the government concludes that while market demand fully captures the marginal benefits of uranium ore concentrate to society, there are additional costs, such as increased risk of cancer, water pollution, and soil contamination. Specifically, the government finds that the marginal external cost (MEC) of uranium mining with respect to the increased risk of cancer is approximated by MECcancer= 70 + 2Q, the MEC of uranium mining with respect to water pollution is approximated by MECwater = Q, and the MEC of uranium mining with respect to water pollution is approximated by MECsoil = 50. Given this information, what equation describes Marginal Social Benefits (MSB)? What equation describes Marginal Social Costs (MSC)? (2)

Part (c) Given the equations for MSC and MSB that you found above, determine the socially optimal equilibrium price and quantity of uranium ore concentrate. Graphically illustrate this equilibrium. (2)

Part (d) What is Total Surplus when the market equilibrium prevails? What is Total Surplus when the socially optimal equilibrium prevails? Which is larger? Why? (2)

Part (e) What per‐unit output tax would correct the market failure in the uranium ore concentrate market (i.e. what tax would induce the market to produce the socially optimal amount of uranium)? In addition to solving for the tax, show this graphically. (2)

Answer 1

market supply = 0.5P-40 market Demande d = 50-011P p=0.52-40 C Suffely) Q+40 = 0.5P P = 80 + 28 Cunnerse MPC = 80+28 S - - 9=50 -0.1P (demand) 0.1p=50-Q P = so - 0.1 0.1 pa 500-100 cuinerse demand) » MSB 500-100 CSScanned with CamScanner

MSC = MEC cancer t MEC match + MEC soit 11 = 70+20 + 0 + 50 MSC = 30 +120 MSBC dewrand) = 500 -10Q MSc = MSB [Social Lyrilibruina] :30 +120 = 500 – 10 Q 139 = 380 /* = 29.231 P = 500-10 (207.692) * = 207.692) (d) || market egreilibrium MP CE MSB | 80 +20= 500-100 120 = 420 Q=35 p=80+2(35) Ip'-1501 Total surplus under market egin = Area of AA BC { x 1500-30) (35) = 7350 Total supues under social dogm = Area of DAEF = f( 500 = 120) (29.231) =5553.89 les canned with CamScanner

Total surplus in market equilibrium is more because more quantity is being sold. Also that ignores the welfare loss associated with externality.

500 MSC 400 MPC 3001 • (29.231, 207.692) 2007 B(35,150) 120 E 1001 MSB 100 7 0 100 2001

(e) when Q=29, 231 s from supply : p= 80+20 =80+2629.931) p=138.462 p*-138.462 = 207,692 - 138,462 69.23 tax - $69.23 After tax supply = 80+20 +69.23 2. DATE. PAGE - p=149.23 +22 MPC = 149.23 +22 - Ittay MPC increases after tax new price = 207.692. new aty = 29.231 CSScanned with CamScanner

-500 MSC MPC+TAX -400 MPC 300 Tax 200 (29.23, 207.69) MSB 1000 1100 100 2007

Let me know if anything is unclear :)