Imagine that the price of input 1 is $16 per unit, the price of input 2 is $25 per unit, and the firm has fixed costs of $60. The firm is in a competitive market where the market price is $240 per unit of output. How much should the firm produce? How much profit does the firm make?
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- (a) Find the conditional input demand function for inputs 1 and 2, as well as the cost function for this firm. (b) What is the firm's marginal cost when it is producing y units of output?A firm produces its output using the following production function: ƒ(x₁, x₂) = x + x ² where x₁ is the amount of input 1 and x2 is the amount of input 2. (a) Find the conditional input demand function for inputs 1 and 2, as well as the cost function for this firm.The manager of Don Teeta Company Limited hires labour (L) and rents capital equipment (K) in a very competitive market. Currently, the wage rate of labour is GH¢2 per hour and capital is rented at GH¢5 per hour, the unit price of the product is GH¢0.75 and total cost of production is GH¢1,000. Suppose the firm’s production function (Q) is as follows: Q = 14K0.5L0.5 + 10 Determine the optimal input usage and the maximum profit.
- Let the production function of a firm is given as q=(x0.5 +y0.5)2 Where x and y are inputs and wx is the price of input x and wy is the price of input y. a) Assume the firm has a limited budget to spend on buying input. Find the cost-conditional input demand function for each input. b) Find the cost function of the firm.Find the MRTS for a firm with production function f(L,K)=(L)^2+vK. Is it diminishing?(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.
- The manager of Don Teeta Company Limited hires labour (L) and rents capital equipment (K) in a very competitive market. Currently, the wage rate of labour is GH¢2 per hour and capital is rented at GH¢5 per hour, the unit price of the product is GH¢0.75 and total cost of production is GH¢1,000. Suppose the firm's production function (Q) is as folows: Q = 14K05L05+ 10 Determine the optimal input usage and the maximum profit.Consider a production function in such a form: Q= f (K,L)= 3KL Calculate the elasticity of substitution (Ϭ) for this firm.The cost function for producing x items is C(x)=x2-3x+625. a.Find the average cost function. b.What is the minimum average cost? c.Find the marginal cost function. d.Is the point of intersection of the average cost and marginal cost function the same which produced the minimum the average cost? 2.Determine where the function f(x)=4x3-3x2+6 is concave and where it is convex. 3.An efficiency study conducted for Spektra Electronics Showed that the number of Base Commander handsets assembled by the average worker t hours after starting work at 8 a.m is given by N(t)=-t2+6t2+15t (0t4) At what time during the morning shift is the average worker performing at peak efficiency?
- A firm has the following production function:q = ƒ (z1, z2) = z1αz2βa. Solve for the firm's cost minimization problem using the Lagrangean method. Verify using the Varian Method.b. Solve for the firm's conditional demand function (simplify) c. Derive the firm's cost function (simplify)A competitive firm uses two variable factors to produce its output, with a production function y = min{ x1, x2 }.The price of x1 is w1 = $8 and the price of x2 is w2 = $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x1. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no output. What is the smallest integer price that would make a firm willing to produce a positive amount?A competitive firm uses two variable factors to produce its output, with a production function y = min{ x1, x2 }.The price of x1 is w1 = $8 and the price of x2 is w2 = $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x1. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no output. What is the smallest integer price that would make a firm willing to produce a positive amount? please solve asap?