UVic Econ 103C with Peter Bell Review for Final Exam Final Lecture Thanks for your engagement this semester. You are quite the group of students! Let s finish off strong here today Suppose Q D (P) = 100-P 2 and Q S (P) = 3 P 2 (as in P-squared). (1) Q D = Q S implies 100-P 2 = 3 P 2 and P* = 5. This is equilibrium price. (2) Q D (5)= 75 and Q S (5) = 75. This is equilibrium quantity. P (3) CS = Q D 10 (P)dP by definition. Here CS = Q D (P)dP = 100P 1 P 5 3 P3 10 5 can calculate and will find CS = 2/3 * 500. P (4) PS = Q S 5 (P)dP by definition. Here PS = Q S (P)dP = P 3 5 0 0 0 = 125. These are the basic types of calculations for general equilibrium. A producer with inventory A producer who waits for prices to pass a threshold Peter Bell, 2014 Page 1 of 5
Two demand curves Combine into one with a kink Q T Q 1 for P > P = { 2 Q 1 + Q 2 for P < P 2 Sorry for nasty notation, but focus on ideas: - P 2 is price where demand curve #2 is zero. - Demand curve #2 is priced out of the market at high prices. A B - This is diagram of policy that forces market to clear at low price. - Pont (A) is when the market clears at the supply curve. - Point (B) is where the market clears at the demand curve. - If both sides are free, then there is a shortage and black market will be higher Peter Bell, 2014 Page 2 of 5
C D - This is diagram of policy that forces market to clear at high price. - Pont (C) is when the market clears at the demand curve. - Point (D) is where the market clears at the supply curve. - If both sides are free, then there is an excess and black market will be lower. What about the Consumer Surplus and Producer Surplus in each case above? Suppose R1(Q) = 50 Q and R2(Q) = (100-Q) Q. Costs are C(Q)=10Q. Note that R1 is of the form R(Q)= P*Q, R2 is of the form R(Q)= P(Q)*Q. (1) Π1(Q) = 50 Q 10 Q = 40 Q. (2) Π2(Q) = (100-Q) Q 10Q = 90Q Q 2. (3) dπ1 /dq = 40 means that optimal Q is always largest possible. (4) dπ2 /dq = 90 2 Q means that optimal Q is 45, if possible. (5) Use notation Q for maximum feasible amount and can say things about optimal choice depending on Q. Peter Bell, 2014 Page 3 of 5
Suppose R(Q)=30Q and costs are C1(Q) = 5Q+1 or C2(Q) = 4Q+3. (1) Π1(Q) =25 Q 1. (2) Π2(Q) = 26 Q 1. (3) For Q>4, see that Π1(Q)<Π2(Q). For Q<4, see that Π1(Q)>Π2(Q). A couple comments on preferences over distributions for profit: - Larger values for mean profit are better, ceteris paribus. - Larger values for variance are worse, known as risk aversion. Reflected in negative coefficient on σ in mean-variance utility - The 5% Quantile is a value in the lower or left tail of the distribution. With 95% confidence, the profit will be higher than this quantile. Thus, bigger is better for the 5% quantile. Suppose utility U = 10 Q1 + Q2. Budget constraint 1 = Q1 + Q2. - Can draw an indifference curve as level set (U constant): Q1=(U-Q2)/10, line with slope -1/10. - Can draw budget constraint as straight line with slope -1. - Draw together and identify optimal quantity consumption: Q1=1, Q2=0. Peter Bell, 2014 Page 4 of 5
PV = CF(k) (1 + r) k k=0 - This is the general statement for calculation of PV, NPV, or Present Worth - Look at the exponents on the discount factors (1+r) -T to determine at what time a cash flow occurs. - Look at the numerator in the series to determine the size of the cash flow. PV = (1 + k 100 ) (1 + r) k k=10 For example, this series describes the following contract: - Cash flows start at time ten and continues to infinity. - The amount starts at 1+10/100 dollars and increases by 1/100 each time step. - The interest rate is always r. - Does it converge? Regardless, useful for illustrating concepts. Suppose Cash Revenue is $100, costs are 20, and depreciation is 10. (1) Taxable income is 100 20 10 = 70. (2) Suppose a 50% tax rate. Then 35 are due in taxes (cash!). (3) The after tax income is 70 35 = 35. (4) The after tax cash flow is 100 20 35 = 45. Note the tax shield is td but be careful how you use it. Example of correct usage: After tax cash flow (45) equals after tax income with zero depreciation (0.5*(100-20)) plus the tax shield (0.5*10). Example of incorrect usage: After tax cash flow (45) does not equal after tax income with depreciation (0.5*(100-20-10)) plus the tax shield (0.5*10). All done! See you all at 9AM, Wednesday August 6 in ECS 123 for the Final Exam. Peter Bell, 2014 Page 5 of 5