Question

Suppose that a firm’s production function is given by Φ(?1,?2)=?1?2. The firm incurs per-unit input costs...

Suppose that a firm’s production function is given by Φ(?1,?2)=?1?2. The firm incurs per-unit input costs of ?1 and ?2 when employing inputs ?1 and ?2, respectively. Derive the firm’s conditional input demand functions ?1?(∙) and ?2?(∙) and the firm’s total cost function ??(∙).

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider a firm whose production technology can be represented by a production function of the form...
Consider a firm whose production technology can be represented by a production function of the form q = f(x1, x2) = x α 1 x 1−α 2 . Suppose that this firm is a price taker in both input markets, with the price of input one being w1 per unit and the price of input two being w2 per unit. 1. Does this production technology display increasing returns to scale, constant returns to scale, decreasing returns to scale, or variable...
A firm has the following production function: ?(?, ?) = ? 3/4?1/4 . A) What is...
A firm has the following production function: ?(?, ?) = ? 3/4?1/4 . A) What is the firm’s Technical Rate of Substitution? B) What is the optimality condition that determines the firm’s optimal level of inputs? C) Suppose the firm wants to produce exactly ? units and that input ? costs $?? per unit and input ? costs $?? per unit. What are the firm’s conditional input demand functions? D) Using the information from part C, write down the firm’s...
for a Production function of a single input Φ(?)=10+(?−1000)^1/3, where ?≥0 denotes the quantity of input...
for a Production function of a single input Φ(?)=10+(?−1000)^1/3, where ?≥0 denotes the quantity of input employed by the firm. Let ?=1 denote the per-unit cost of the input incurred by the firm. Derive the firm’s total cost function ??(∙).
A firm’s production function is given as y=(x1)^(1/2) * (x2-1)^(1/2) where y≥0 for the output, x1≥0...
A firm’s production function is given as y=(x1)^(1/2) * (x2-1)^(1/2) where y≥0 for the output, x1≥0 for the input 1 and x2≥0 for the input 2. The prices of input 1 and input 2 are given as w1>0 and w2>0, respectively. Answer the following questions. Which returns to scale does the production function exhibit? Derive the long-run conditional input demand functions and the long-run cost function.
Suppose a firm’s production function is given by Q = L 1/2 , K 1/2. a)...
Suppose a firm’s production function is given by Q = L 1/2 , K 1/2. a)   Suppose the firm has a fixed cost FC=6, the price of labor is w = 64 and the price of capital is r = 4. Derive the firm’s total cost function, TC(Q). b)   What is the firm’s marginal cost? c)   Graph the firm’s isoquant for Q = 20 units of output. On the same graph, sketch the firm’s isocost line associated with the total...
2 .Suppose the production function of a firm is given by f (x1, x2) = 2x1...
2 .Suppose the production function of a firm is given by f (x1, x2) = 2x1 + 4x2 (a) Calculate the conditional demand functions of the firm assuming w1 = 2; w2 = 3, and y = 8 (b) Calculate the minimum cost of the firm to produce 8 units of the good when w1 = 2 and w2 = 3
5. Suppose a firm’s production function is Q = K.25L.25. The MPK = .25K-.25L.25 and MPL...
5. Suppose a firm’s production function is Q = K.25L.25. The MPK = .25K-.25L.25 and MPL = .25K.25L-.25. The price of K is 1 and the price of L is 2. • Derive the conditional demand functions for K and L • Derive the long-run cost function
True of False “If a firm’s total cost function is given by ??(?,?,?)=√??? where the variables...
True of False “If a firm’s total cost function is given by ??(?,?,?)=√??? where the variables ? and ? denote the (per-unit) input prices of labor (ℓ) and capital (?), respectively, then its “conditional” demand for labor is increasing in ?.
A firm’s production function is q = 10KL with per unit input prices for labor w...
A firm’s production function is q = 10KL with per unit input prices for labor w = 3 and capital r = 2. Support your answers with a graph of isoquant-isocosts. a. Calculate the least-cost input combination of L and K to produce 60 units of output. b. Suppose the wage decreases to $2. How does this affect input use holding constant output at 60? c. What are the total costs of producing the two output levels in parts (a)...
A firm’s production function is Q(L,K) = K^1/2 + L. The firm faces a price of...
A firm’s production function is Q(L,K) = K^1/2 + L. The firm faces a price of labor, w, and a price of capital services, r. a. Derive the long-run input demand functions for L and K, assuming an interior solution. If the firm must produce 100 units of output, what must be true of the relative price of labor in terms of capital (i.e. w/r) in order for the firm to use a positive amount of labor? Graphically depict this...