The Cost-Minimization problem For given Wi, W2 and y, the firm's cost-minimization problem is to solve min W1X1+w2X2 X1,X2≥0 subject to f (X1, X2)=y
The Cost-Minimization Problem For 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 + 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) 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 The 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）. The (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 Given W1, W2 and y, how is the least costly input bundle located? And how is the total cost function 成本函数) computed?
Conditional Input Demands Given w1 , w2 and y, how is the least costly input bundle located? And how is the total cost function （ 成本函数）computed?
Iso- cost lines(等成本线) A 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） A curve that contains all of the input bundles that cost the same amount is an iso-cost curve. E.g., given w1 and w2 , the $100 isocost line has the equation w1 x1 + w2 x2 = 100
Iso-cost Lines Generally, given W, and w2, the equation of the sc iso-cost line is W1X1FW2X2=C .e W1 X2 w2 X2 Slope is -W,w2
Iso-cost Lines Generally, given w1 and w2 , the equation of the $c iso-cost line is i.e. Slope is - w1 /w2 . x w w x c w 2 1 2 1 2 = − + . w x w x c 1 1 + 2 2 =