Derive the long-run cost function for the constant elasticity of substitution production function q = (Lρ + Kρ)d/ρ
Please explain the math to this. I don't understand the derivation of this.
Derive the long-run cost function for the constant elasticity of substitution production function q = (Lρ...
2. Marginal products, RTS, and elasticity of substitution: Consider the following production function: q=k *11/4 a. For some w, y, use the Lagrangean method to derive demand functions by finding the cost-minimizing combinations of k and I in terms of q, w, and y (so the cost function is the objective function, and the production function is the constraint). (10 points) b. What is the rate of technical substitution (RTS) for this function? (5 points) C. Presume that the firm...
Consider the constant elasticity of substitution (CES) production function F(xi, x2) A (ao lix;" + a2x3)'/ρ. Show that F has constant returns to scale when 10-0.
Let q = L½k½ denote the production function for a firm making long-run decisions, that is K (capital) and L (labor) are now variable. a. Place k on the Y-axis and L on the X-axis and illustrate an isoquant when q=100.b. Derive an expression for the MRTS (the marginal rate of technical substitution) for any level of q.
Suppose the production function of a firm is given by q = L1/4K1/4. The prices of labor and capital are given by w = $10 and r = $20, respectively. a) Write down the firm's cost minimization problem. b) What returns to scale does the production function exhibit? Explain c) What is the Marginal Rate of Technical Substitution (MRTS) between capital and labor? d) What is the optimal capital to labor ratio? Show your work. e) Derive the long run...
for a production function q = 3L + 5K, what's the long run labor demand, long run capital demand, and long run total cost in terms of q, w, r? I need a step by step defination. I got w/r = 3/5 and I'm stuck.
Please solve the above sum
(B) Q = 50k E (d) A firm in a perfectly competitive industry has the following long run cost function C(q) q-60q+1500q O) If the firm can sell its output at p Rs. 975, how much will it produce to maximise profit? (i) Is the output of the firm in (i)compatible with industry equilibrium? (Gii) If the industry is that of constant average cost, derive the equation for the long run supply curve of the...
Suppose the production function is given as Q = VLK. Suppose also that the price of labor w = 10 and the price of capital r = 40 1) Derive the equation of the isoquant corresponding to this production function? 2) What type of return to scale does this production exhibit? 3) Does this production function exhibit a diminishing MRTS? Why? 4) Based on this production function, is the law of diminishing marginal returns satisfied? 5) Derive the demand curves...
The production function for a firm is Q = AK^αL^β, and its user cost of capital and labor is r and w, respectively. Find the elasticity of substitution for this production function. Is it a constant? Show your work.
What is the long-run cost function for a fixed-proportions production function when it takes five units of labor and four units of capital to produce one unit of output? Describe the long-run cost curve. Multiply the inputs by their prices and sum to determine total cost Let w be the cost of a unit of labor and r be the cost of a unit of capital. The long-run cost function C(q) for the fixed-proportions production function in terms of w,...
Derive the elasticity of substitution for the Cobb-Douglas production Fonction. f(L,K) = ALαKβ