Ecomonics 10A
by Alexander Berger
1. Inter-temporal Consumption
1.1. U=C1C2
1.2. BC in Future Value with Inflation Assuming Prices are $1: (1+r)*C1 + (1+pi)*C2 = (1+r)m1 + m2
1.3. Tang: MRS = Slope of BC -(1+r) OR -(1+r)/(1+pi)
1.4. Present Value of Future $: $x/(1+r)
1.5. Future Value of Present $: (1+r)*$x
2. Consumer Demand
2.1. Cobb Douglas
2.1.1. U=XY
2.1.2. BC: P1*X + P2*Y = m
2.1.3. Tang: MRS = P1/P2
2.2. Leontief
2.2.1. U= min [X/a, Y/b]
2.2.2. BC: P1*X + P2*Y = m
2.2.3. Tang: X/a = Y/b
2.3. Linear
2.3.1. U=X + Y
2.3.2. BC: P1*X + P2*Y = m
2.3.3. Tang: Doesn't Exist
2.3.4. Compare MRS to Price Ratio: If MRS = Price Ratio, any Bundle is OK IF MRS > Price Ratio, Consume all X If MRS < Price Ratio, Consume all Y
3. Gambles and Insurance
3.1. Sum of the Weighted Utilities
3.2. Sum of Weighted Utilities of States of Nature
4. SE/IE
4.1. SE= B-A IE= C-B
4.2. Steps: 1) Find Demand functions for X and Y 2) Plug into Utility function and set it equal to the original utility. 3) Solve for Hicks Adjusted M 4) Plug M into the demand functions to find B
5. Firm Profits/Costs
5.1. Output Choice: Price = Marginal Cost
5.2. Shutdown Decision: Long Run: TR < LTC Short Run: TR < SVC
5.3. Cost Curves
5.3.1. Q=LK
5.3.2. Output Constraint: Q=LK
5.3.3. Tang: MPL/MPK = w/r
5.4. Short Run Profit Max
5.4.1. Q=LK (K Fixed)
5.4.2. FOCs: P*MPL=w P*MPK=r
5.4.3. K is fixed No Tangency Solve for L*
5.5. Long Run Profit Max
5.5.1. Q=LK
5.5.2. Tang: MPL/MPK = w/r
5.5.3. FOCs: P*MPL=w P*MPK=r
5.6. Long Run Cost Minimization
5.6.1. Q=LK (Q Fixed)
5.6.2. Tang: MPL/MPK = w/r
5.7. Short Run Cost Minimization
5.7.1. Q=LK (Q&K Fixed)
5.7.2. Just Solve for L