Topics Today (4/9/13)  Classroom game  Managing open access renewable resources 1Renewable Resources  Wind energy, solar energy (flow of energy this period unrelated to flow of energy last period)  Plants and animals (growth depends on current stock)  Groundwater (some aquifers are recharged) 2Biological growth Sk growth stock The next few slides build intuition about the relationship between stock levels, growth and harvest … The main reason to consider this graph is to examine the difference between the traditional goal of fisheries management and the goal typically advocated by economists …maximum sustained yield vs. efficient sustained yield Carrying capacity 3Biological growth growth stock Point of critical dispensation Sk 4Sustained yield harvest Stock BSASHarvest level h’ Growth, harvest Growth curve MSYSHarvest level hMSY 0 Stock dynamics are given by : St+1= St + G(St ) – Ht Sustained yield harvest is the harvest where the stock doesn’t change over time: St+1= St And so it must be that for sustained yield harvest, G(St ) – Ht Sk 5There are many sustained yield stock levels for a biological renewable resource k Stock Harvest level h’ Growth, harvest Growth curve harvest level ĥ ˆASMSYSHarvest level hMSY 0 ˆBSASBS6A few questions about the dynamics of the stock Stock Harvest level h’ Growth, harvest Growth curve harvest level ĥ ˆASMSYSHarvest level hMSY 0 ˆBSASBSQ1: If the stock is at SMSY and harvest is constant over time at h’, where does the stock end up in the long run, i.e. what is the sustainable stock level? A=SMSY B=S’A C=S’B D=0 E=NIW 7A few questions about the dynamics of the stock Stock Harvest level h’ Growth, harvest Growth curve harvest level ĥ ˆASMSYSHarvest level hMSY 0 ˆBSASBSQ2: If the stock is at SB’ and harvest is constant over time at h-hat, where does the stock end up in the long run? A=SMSY B=S’A C=SB-hat D=0 E=NIW Sk 8A few questions about the dynamics of the stock Stock Harvest level h’ Growth, harvest Growth curve harvest level ĥ ˆASMSYSHarvest level hMSY 0 ˆBSASBSQ3: If harvest is constant over time at h’, what is the range of stock levels at which the long run sustained yield stock level is S’A? A=SMSY -S’A B= S’B -Sk C= S’A -Sk D= S’B - S’A E=NIW Sk 9Simple economics of fishery sustained yields (fishery sustainability) Net benefit in a given period: p·h – mec(S) ·h What would be the present value of sustained yield net benefits at SMSY if the discount rate is r and the stock is at SMSY in the current period? Stock BSASGrowth, harvest Growth curve MSYSHarvest level hMSY 0 Sk 10Simple economics of fishery sustained yields (fishery sustainability) Which stock level, S’A or S’B , would generate greater sustained yield net benefit? Net benefit in a given period: p·h – mec(S) ·h Stock BSASHarvest level h’ Growth, harvest Growth curve MSYSHarvest level hMSY 0 Sk 11Maximum sustained yield and the simple economics of fishery sustained yields (fishery sustainability) Is it possible that the sustained yield harvest at S’A generates a greater present value of net benefits than the sustained yield harvest at SMSY? This is why economists argue against management for maximum sustained yield; society can do better Stock BSASHarvest level h’ Growth, harvest Growth curve MSYSHarvest level hMSY 0 Sk 12The Efficient Sustained Yield Stock Level Suppose S’A is the efficient sustained yield stock level, and the current stock level lies above the efficient sustained yield stock level. Will a market free of government intervention generate the efficient sustained yield stock level? Stock BSASHarvest level h’ Growth, harvest Growth curve MSYSHarvest level hMSY 0 Sk 13Game  You are the captain of a fishing boat  Your objective is to maximize your profit over time by choosing the number of months at sea in each year (E) over your 15-year fishing career.  There is an upper limit to the number of months at sea per year (E must be no more than 4)  Information concerning your profits:  Your profits are the difference between harvest revenues and costs  Each month at sea costs $200  Price of fish is $1  Harvest of fish depends on the stock of fish and the days you spend at sea:  H = E ∙(a ∙ S) = 0.2∙E ∙S  At the start of each year you know the current fish stock S  Discount rate=0 14Game  Your objective is to maximize profits over your career  Summary of profits  Profits=price x harvest –cost/month x months  => Profits = 1∙ (0.2 ∙ S) ∙ E – 200 ∙ E  Or, Profits = (0.2∙ S – 200) ∙ E  Two randomly selected fishing vessels obtain a cash reward equal to a fraction of their present value of profits at the end of the game (if negative profits, you pay me).  Game will be up to 15 years  I will show you two things a the end of every year: the stock at the end of the year (which is the stock at the start of next year), and your profits. Months Fishing (E) A=0 B=1 C=2 D=3 E=4 15Game  Logistic growth function 05101520250 500 1000 1500 2000 2500 3000