cost minimization

slope of isocost

-wK/ wL

Factor Price Ratio

1. the amount of input good 2 the firm MUST give up to get one more unit of input good 1 and maintain same cost level. 2. the amount of input good 2 a firm will receive if he gives up one unit of good1, sells it and uses the proceeds to purchase more of input good 2. 3. (the negative of) the slope of the isocost line w/ input good 1 on the x-axis 4. if prices are FIXED, and nothing is being given away for free, factor price ratrio1,2: w1/w2

Efficiency & "strict-free disposal" ensure which properties of isoquants?

1: Not upward sloping 2: Not crossing 3: Thin 4: higher quantities as you move away from origin 5: bowed in towards origin (because of convexity)

Lagrangian for production function

L = w1x1 +w2x2 + λ(q - f(x1, x2)) want to minimize w1x1 + w2x2 constraint: q - f(x1, x2)

Marginal rate of technical substitution

MRTSx1, x2: 1. MAX amount of input 2 the firm would be WILLING TO GIVE UP to get one more unit of input 1, while keeping total output the same 2. the MIN amount of input 2 the firm would NEED TO RECEIVE to give one unit of input 1, while keeping total output the same. 3. (the negative of) the derivative of the isoquant x2 = f(x1)

Convexity in production set

a balanced production plan is at least as efficient as an unbalanced production plan.

No Free Lunch

a production function in which it is impossible to produce output without using any inputs

Conditions for Lagrangian

function is/ has: - continuous - derivative that is continuous - quasi-convex - defined by an equality - defined by a convex f'n

Isoquant

graphical set of all bundles of input that allows a firm to produce the same level of ouput

Isocost lines

graphical set of input good bundles that cost the same amount

cost minimizing input blend

if firm's underlying production set is CONVEX, displays STRICT-FREE DISPOSAL, and is EFFICIENT, then if firm USES BOTH INPUT GOODS, then its cost minimizing blend to produce a specified level of output will be at a point such that the slope of the firm's isoquant is identical to the slope of the isocost line passing through that point. f1/f2 = w1/w2

Isocost Line slope

if input prices stay the same, different isocost lines will have identical slopes, but represent different total cost levels. the farther an isocost line is from the origin, the higher the total cost level.