The cost-Minimization problem For given W,, W2 and y, the firms cost-minimization problem is to solve min W1X1+W2X 2 X1,X2≥0 subject to f(x1, X2)=y
The Cost-Minimization Problem uFor given w1 , w2 and y, the firm’s cost-minimization problem is to solve min x ,x w x w x 1 2 0 1 1 2 2 ³ subject to f (x ,x ) y. 1 2
The cost-Minimization problem The levels x,*(W1, W2,y)and x,"W,,W2 y) in the least-costly input bundle are the firm's conditional demands for inputs 1and2(条件要素需求) o The( smallest possible) total cost for producing y output units is therefore c(W1,W2,y)=w1x1(W1,W2,y) +w2X2(W1,W2,y)
The Cost-Minimization Problem uThe levels x1 *(w1 ,w2 ,y) and x1 *(w1 ,w2 ,y) in the least-costly input bundle are the firm’s conditional demands for inputs 1 and 2 （条件要素需求）. uThe (smallest possible) total cost for producing y output units is therefore c w w y w x w w y w x w w y ( , , ) ( , , ) ( , , ). * * 1 2 1 1 1 2 2 2 1 2
Conditional Input demands 4 Given W1, W2 and y, how is the least costly input bundle located? c And how is the total cost function 成本函数) computed?
Conditional Input Demands uGiven w1 , w2 and y, how is the least costly input bundle located? uAnd how is the total cost function （ 成本函数）computed?
Iso- cost lines(等成本线) PA curve that contains all of the input bundles that cost the same amount is an iso-cost curve +E.g, given W, and W2, the $100 iso cost line has the equation w1X1+w2x2=100
Iso-cost Lines （等成本线） uA curve that contains all of the input bundles that cost the same amount is an iso-cost curve. uE.g., given w1 and w2 , the $100 isocost line has the equation w x w x 1 1 2 2 100
Iso-cost lines Generally, given W, and w2, the equation of the Sc iso-cost line is WiX1+W2X2=C Le W1 X2 X1+ w2 2 ◆ Slope Is-WW2
Iso-cost Lines uGenerally, given w1 and w2 , the equation of the $c iso-cost line is i.e. uSlope is - w1 /w2 . x w w x c w 2 1 2 1 2 . w x w x c 1 1 2 2