A)
Each point on the expansion path is a point of tangency between an isoquant and an iso-cost line. Therefore, at each point on the expansion path, we have the numerical slope of the isoquant = numerical slope of the isocost line.
Therefore,
B)
Yes, this function is homothetic. The basic feature of a homothetic function is that the expansion path of these functions are linear and we can see in in the pic ( attached) the expansion path is linear in z1 and z2.
1. A firm has the production function y-Z1Z2 and faces input prices W1 6 and w2-...
A firm has the production function y= f(x1,x2)= 0.25x11/2 x21/2 . Input prices are w1=$4 and w2= $16 a) Use the technical rate of substitution, the input price rate, and the production function to compute the conditionial input demand fucntion x1(y) and x2(y). b) Compute the firm's long run cost function c(y).
A firm has decreasing returns production function f(x1, x2)=(x1)1/6(x2) 1/3 and faces input costs w1=1 and w2=2. Find the cost function.
please show all work, thanks! Problems 1 a) A firm has the production function y = 22212 and faces input prices W1 and w2. Derive the conditional input demand functions for both inputs. b) If W, = $5 and W2 = $10, what is the minimum cost of producing 27 units of output?
2. A firm has the production function y - z1+ 2z2 Input prices are w 2 and w2 3. a) What is the equation of the OEP? b) Is this production function homothethic?
Consider a firm with the cost function c(y, w1, w2) = y2(w1 + w2), where wi denotes the price of inputi, i = 1, 2. Let p denote the output price. Derive the output supply function y(p, w1, w2), and the input demand functions xi(p, w1, w2), i = 1, 2
3. A firm has the production function y 5Z1 + Z2- Input prices are w,-9 and W2 = 3 a) What is the cost minimizing input bundle? b) What is the minimum cost to produce 100 units of output?
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