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Department of Agricultural and Resource Economics University of California at Berkeley ENV ECON 1 P. Berck A. Dey (TA) INTRODUCTION TO ENVIRONMENTAL ECONOMICS AND POLICY Problem Set No. 1 (Solutions by Joyce Luh) Problem 1 1. Demand and supply for milk: $P Supply x 10 — • 8 — x • 6— • E 4— x 2 —x Floor • Surplus | | | 20 D 40 60 Q F P x Demand • | | | 80 100 120 S Q Q F The demand curve shows how the quantity that consumers are willing to purchase varies with the price of milk. The supply curve shows how the quantities that firms are willing to sell vary with the price of milk. 2. Equilibrium price = $5. Equilibrium quantity = 50 units of milk (E). This point is an equilibrium because, at this price, there is no excess supply or demand. 3. Price is fixed at $7 (PFloor). At the fixed price, consumers are willing and able to buy D S just 30 units ( QF ) while firms are willing and able to sell 80 units ( QF ). Thus, at the fixed price, there are 50 units (80 - 30) of surplus production. 4. New demand = old demand + 50 percent = 1.5 x (old demand). P Q - new demand 10 8 6 4 2 0 30 60 90 120 $P Supply x $10 — • 8 — • x • 1 • 6— E •x • x E0 • 4— D - new • 2 —x • D - old | 20 | | 40 60 | 80 | | 100 120 Q The shift in demand results in the new demand schedule and curve plotted above. The equilibrium price and quantity shifts from E0 to E1 on the graph. The new equilibrium price increases to about $5.83, and the new equilibrium quantity increases to about 62.5 units. While the supply curve has not changed, the eqm quantity supplied has increased about 12.5 units. 5. The bovine growth hormone will allow firms to profitably produce more milk at all price levels. Thus, the supply curve will shift out. Assuming that the hormone does -2- not alter the quality of the milk produced by cows, demand will not change. However, the outward shift in supply will lower price and increase both the quantity supplied and the quantity demanded. P S S 1 .. E P0 P1 0 E 1 D Q 0 Q1 Q Problem 2 1. First, the supply of anchovies shifted in with their disappearance off the coast of Peru. This caused the equilibrium price to increase dramatically and the quantity demanded to decrease. Graphically: $ Supply - post-1972 Supply - pre-1972 P1 P 0 D - anchovies Q1 Q0 Q - anchovies 2. Because anchovies and soybeans are both rich in protein, they are substitute goods. Thus, the new higher price in anchovies caused the demand for soybeans to shift out, increasing both the price and quantity supplied of soybeans. Graphically: -3- $ S - soybeans P1 P0 D - post-1972 D - pre-1972 Q0 Q1 Q - soybeans 3. Because soybeans are an input into the production of cattle (i.e., you need soybeans to make cows), the supply of cattle in the cattle market shifted in with the increase in the price of soybeans. The result was higher cattle prices and a lower quantity of cattle demanded. Graphically: $ S - post-1972 S - pre-1972 P1 P 0 D - cattle Q1 Q0 Problem 3 P = 120 - 3Qd demand P = 5Qs supply In equilibrium, Qs = Qd = Q*, so P = 120 - 3Q* P = 5Q* 5Q* = 120 - 3Q* -4- Q - cattle 8Q* = 120 Q* = 15. P = 120 - 3Q* = 120 - 3(15) = 75. Checking answer: P = 5Q* = 75. Equilibrium price = 75cents per pound Equilibrium quantity = 15 ml pounds. Problem 4 Suppose that the representative home demander is in the 35 percent income-tax bracket. If the governmental subsidy is removed, the effective price of a home increases 25 percent. Demand elasticity = percent change in quantity demanded divided by percent change in price. Therefore, %Q 1.2 %Q 25% 1.2% 30%. 25% So quantity demanded decreases 30 percent. (An alternative and perhaps better answer. If the price of housing were 100% before the reduction, it would be 75% after it. Now on canceling the reduction it goes from .75 to 1.00, a 33% change. Now 33% (1.2) = 39.6 percent. Problem 5 1. Original P = P0 = $6 per unit. New P = P1 = $6.06 per unit. Average P = P = $6.03 per unit. Original Q = Q0 = $600,000/$6 = 100,000. New Q = Q1 = $594,000/$6.06 = 98,020. Average Q = Q = 99,010. Elasticity based on averages (as in Lipsey and Courant). -5- Elasticity of demand = (percent change in Q)/(percent change in P). Percent change in Q = (98,020 - 100,000)/99,010 = -2 percent. Percent change in P = (6.06 - 6)/6.03 = 1 percent. Elasticity of demand = (percent change in Q)/(percent change in P) = (-2 percent)/(1 percent) = 2. 2. Demand has not changed, so we cannot calculate an elasticity of supply (must have two points on the same curve to calculate an elasticity). 3. New equilibrium S new En $6.06 Soriginal Eo Old equilibrium $6 D Q 90k 100k Regions + = old expenditure = $600 K Regions + = new expenditure = $594 K. -6-