Profit Max Flashcards
How are Profits calculated?
Profits = Revenue – Costs π = ∑(pi•yi) - ∑(wi•xi) --- wi = Input Prices, pi = Output Prices
If Input 2 level is fixed at x¯2 - What is SR Profit Max?
SR: max π = pƒ(x1,x¯2) - (w1•x1) - (w2•x¯2)
FOC: ∂π / ∂x1 = 0 ==> p•MP1(x1*,x¯2) = w1
–Value of MP of a Factor = Factor’s Input Price
How can Profits be Increased if p•MP1 > w1 ?
Increased x1 –> Decreased MP –> Decreased p•MP1(x1*,x¯2)
How can Profits be Increased if p•MP1 < w1 ?
Decreased x1 –> Increased MP –> Increased p•MP1(x1*,x¯2)
Derive Slope of Prod. Func. from p•MP1(x1*,x¯2) = w1
MP1(x1*,x¯2) = w1/p
= Also Slope of Iso-Profit Line
Define Iso-profit Line
Gives all Combinations of Input Goods + Output goods that give Same Profit Level
What is the Iso-profit Line given π = py - w1x1 - w2•x¯2?
y = π/p + (w2/p)(x¯2) + (w1/p)(x1)
What is the Slope of Iso-profit Line y = π/p + (w2/p)(x¯2) + (w1/p)(x1)?
Slope = w1/p
= Slope of Prod. Func.
In SR- If Output Price changes + Firm can sell at Higher Price, what happens to Prod. + Profits in SR?
Increased p –> Increased Production due to higher Profitability –> Increased Profits
In SR- If Input Price w1 Increases, what happens to Profits?
Increased w1 –> Increased Cost of Input 1 –> Decreased Demand for Input 1 –> Decreased SR Output
∂x1/∂w1 < 0 - Negative Relationship - Increased w1 –> Decreased x1
How is LR Profit Max found?
All factors Variable max π = p•f(x1,x2) - w1x1 - w2x2 => FOCs: ∂π/∂x1 = 0 , ∂π/∂x2 = 0 ==> pMP1 = w1 , pMP2 = w2 MR = MC for All Inputs pMPi = MR , wi = MC
If Firm chooses LR Profit Max Output: y* = f(x1, x2)- Why do Constant R.t.S mean Profits = 0?
π* = py* - w1x1* - w2x2*
Constant R.t.S + Positive Profits – Imply firm can Double Output –> Double Profits
– Contradicts that Initial Output was Profit Maximising
LR π* = 0 for Competitive Firm
