"There are three kinds of economics: Greek-letter, up-and-down, and airport." Paul Krugman

Formulas, Equations, and Definitions to Remember

• Present Value
• Elasticity
• Production and Cost: Output
• Revenue and Profit: Output
• Inputs

Present Value Equation 

Describes the relationship between the values at two points in time.  Actually it can be thought of as an equation with four unknowns, and all you need to do is solve for the one unknown.   Below is the equation where future value (FV) is the unknown.  

FV = PV*(1 + g)^T

Where:

• PV = Present Value ( value at beginning of the period)
• FV = Future Value ( value at the end of the period)
• g = Average growth rate per period
• T = Number of time periods

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Elasticity 

The formulas for demand and supply elasticities are:

• Income elasticity of demand
  • definition: responsiveness of demand to income change
  • formula: e_y = %DQ/%DY
• Cross-price elasticity of demand
  • definition: responsiveness of demand (good A) to change in price of another good (price of B)
  • formula: e_c = %DQ_A/%DP_BBB
• Own-Price elasticity of demand
  • definition: responsiveness of demand to price change
  • formula: e_p = %DQ/%DP
  • possibilities
    • inelastic: unresponsive = | e_p | < 1
    • elastic: responsive | e_p | > 1
    • unitary elastic: | e_p | = 1
• Own-Price elasticity of supply
  • definition: responsiveness of supply to price change
  • formula: e_ps = %DQ_s/%DP/

Relationship between price elasticity and revenue

• DR = Q*(1+e_p)*DP

• DR = P*(1+1/e_p)*DQ

  or in percentage terms

• %DR = (1+e_p)*%DP

• %DR =(1+1/e_p)*%DQ

Production and Cost 

short-run production concepts

• Total (physical) product
  • Definition: amount of output obtained from given amount of input
  • Graph: vertical axis (units of output)  : horizontal axis (units of input)
• Average (physical) product:  
  • Definition: amount of output obtained per unit of input
  • Formula:   Output / Input
  • Graph: vertical axis (average product)  : horizontal axis (units of input)
• Marginal (physical) product:  
  • Definition: additional output obtained by 1 more unit of input
  • Formula:   DOutput /  DInput
  • Graph: vertical axis (marginal product)  : horizontal axis (units of input)
    • Diminishing marginal product: as input use expands the marginal product begins to decline

short run cost concepts

• Total Cost (TC): 
  • Definition: all costs of production (Fixed costs plus variable cost)
  • Formula: Fixed Cost + Variable Cost  (TC = FC + VC)
  • Graph: vertical axis (Total cost)  :  horizontal axis (Output)
• Fixed Cost (FC): 
  • Definition: all costs of production (Fixed costs plus variable cost)
  • Formula: Fixed cost 
  • Graph: vertical axis (Fixed cost)  :  horizontal axis (Output)
• Sunk Cost (SC):
  • Definition: costs of resources that have already been incurred and will not change regardless of any current or future decisions
• Variable Cost (VC):  
  • Definition: costs of production that vary with output
  • Formula: Variable cost 
  • Graph: vertical axis (Variable cost)  :  horizontal axis (Output)
• Average Cost (AC): 
  • Definition: costs per unit of output
  • Formula: Total cost / Output  (AC = TC/Q)
  • Graph: vertical axis (Average cost)  :  horizontal axis (Output)
• Marginal Cost (MC):
  • Definition:  additional costs of producing more output
  • Formula: D Total cost / D Output
  • Graph: vertical axis (Marginal cost)  :  horizontal axis (Output)
• Average Variable Cost
  • Formula: Variable cost / Output  (AVC = VC/Q)
•  Average Fixed Cost
  • Formula: Fixed cost / Output  (AFC = FC/Q)

long run production and cost concepts

• decreasing returns to scale: if we double all inputs and output less than doubles
• constant returns to scale: if we double all inputs and output doubles
• increasing returns to scale: if we double all inputs and output more than doubles

• increasing cost industry: as we expand output, average cost rises
• constant cost industry: as we expand output, average cost remains constant
• decreasing cost industry: as we expand output, average cost falls

Revenue and profit 

Revenue and profit relationships

• Total Revenue: relationship between sales revenue and output = relationship between sales revenue and output =
  • Definition: relationship between sales revenue and output 
  • Formula: Price * Quantity  (P x Q)
  • Graphs: vertical axis (Revenue)  : horizontal axis (Output)
• Average Revenue:
  • Definition: amount of revenue obtained per unit of output 
  • Formula: Revenue / Output (TR/Q)
  • Graphs: vertical axis (Average Revenue)  : horizontal axis (Output)
• Marginal Revenue:
  • Definition: additional revenue from selling more unit of output 
  • Formula: D Revenue / D Output (DTR / DQ)
  • Graphs: vertical axis (Marginal Revenue)  : horizontal axis (Output)
• Total Profit: 
  • Definition: relationship between profit and output 
  • Formula:  Total Revenue  - Total Cost  (TR - TC)
  • Graphs: vertical axis (Profit)  : horizontal axis (Output)
• Marginal Profit:   Marginal profit 
  • Definition: additional profit obtained by producing and selling 1 more unit of output
  • Formula:  D Profit / D Output (DP / D Q)
  • Alternative formula:  MP = MR - MC
  • Graphs: vertical axis (Marginal Profit)  : horizontal axis (Output)

Logic of Profit Maximization: implications of decision to raise output

1. Profit = Revenue - Cost
2. Revenue: depends on demand
3. Cost: depends on input use and costs
4. Marginal revenue (MR) is the additional revenue of the decision
5. Marginal Cost (MC) is the additional cost of the decision
6. Marginal Profit (MP) = MR - MC is the additional profit of the decision
7. MP > 0 means that the decision will increase profit
8. MP < 0 means that the decision will decrease profit
9. MR = MC  (MP = 0) means the maximum profit choice
10. Since FC does not affect MC, then FC does not affect optimal choice

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Inputs 

Optimal input choice rules for profit maximizer

Short run

MRP_A =  MR_X * MP_A  = P_A

Long run

MRP_A /P_A = MRP_B /P_B

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