ex Production function is f(x, 1x2)= min(x,, 2x₂ Dwhat are the conditional factor demand of y = 10 2 ② if the firm faces w, and w₂ as input prices, what is the cost function?

Suppose that the production function for Hannah and Sam's home remodeling business is            Q = F(L,K)            Q = 10L0.1K0.4.Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $1,000 per week.a. What is the least-cost input combination for remodeling 400 square feet each week?      Instructions: Round your answers to 2 decimal places.      units of labor and  units of capital.  b. What is the total cost?         Instructions: Round your answer to 2 decimal places.    $  .revised jrl 08-11-2011

(a) For the cost function C(w1, w2, y) = 2y²w} w, calculate the Allen elasticity of substitution between the two inputs at the cost-minimizing input point (xf(w1, w2, y), a(w1, w2, y)). (b) Consider the production function f(r, y, z) = Vry + rz+ yz. Find the scale elasticity SE at (x, y, z) = (1,2, 3), (5, 1,6), (6, 6, 6) and determine if the pro- duction function is IRTS, CRTS, or DRTS locally at each point. (c) A profit maximizing firm in the market operates where the production exhibits decreasing return to scale (DRTS). Is this market in its long-run equilibrium? Justify your answer. (d) Suppose that there are the infinite number of potential firms that produce the identical output good y under the cost function C(y) = + 3. Assume free entry and exit. Find the long-run equilibrium output price p, the amount of the output that each firm in the market produces in the long-run equilibrium, and the value of profit that each firm earns in the equilibrium.