1. Find the cost minimizing input demand functions (x₂ (w, q)) and the cost function (c(w, q)) for the following production functions: 2132 1/3 a. f(x) = x₁
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- (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 total revenue function for a product is given by R=655x dollars, and the total cost function for this same product is given by C=19,250+70x+x2, where C is measured in dollars. For both functions, the input x is the number of units produced and sold. a. Form the profit function for this product from the two given functions. b. What is the profit when 25 units are produced and sold? c. What is the profit when 43 units are produced and sold?1 A smartphone repair firm in Boston has a production function for producing phone repairs, q, defined as, — 4 -L1/2K 1/2, where L is labor measured in hours worked, and K is the number of useful tools used in the repair process. The market wage for a phone repairperson, w, is $25 per hour. The tools could be sold at a secondhand market for $4 (r). Find the (variable) cost function:. Submit your answers as a single PDF. Please try and keep solutions tidy.
- (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?The total revenue function for a product is given by R=655x dollars, and the total cost function for this same product is given by C=19,250+70x+x2, where C is measured in dollars. For both functions, the input x is the number of units produced and sold. a. Form the profit function for this product from the two given functions. b. What is the profit when 25 units are produced and sold?1) The Cobb-Douglas production function is y = 12 with a > 0 and 3 > 0. Show that MP₁ = ay/2₁, MP₂= By/22. What is the MRT S21? How does it vary with: (a) y: (b) 2/1. 2) Show that the cost function for a firm with the constant returns Cobb-Douglas production function y = Actis given by C(p, y) = ypip-B, where B is a function of A and a only. Derive the conditional input demands.
- E Let the demand function for a product be given by the function D(q) = -1.65g + 270, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $4, 000 and variable costs are $3 per item produced. If 96 items are produced and sold, find the following: A) The total revenue from selling 96 items (to the nearest penny). Answer: $ B) The total costs to produce 96 items (to the nearest penny). Answer: $ C) The total profits to produce 96 items (to the nearest penny. Profits may or may not be negative.). Answer: $ Question Help: C ME PE Video 66°F Mostly cloudy*Find the elasticity of scale and the elasticity of substitution for the CES production function f(x1,x2) = (x{ + x%)¯,where 0 #p<1.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.
- f(k,l) = 1/3k1/3, the A firm is faced with a production technology that uses capital and labor: q = price of labor is w, and the price of capital is r. (a) Write down the cost minimization problem and determine the contingent input demand functions: 1(w, r, q) and k°(w, r, q). Also, derive the cost function C(w, r,q). (b) The firm operates in a perfectly-competitive market and faces a market price of p. Write down the firm's profit function. Solve the maximization problem to determine (1) input demand, that is, the demand for labor and capital as a function of w, r, and p (2) the output supply function, q as a function of w, r, and p.Given the input-output matrix below, find the output matrix if final demand changes to 600 for water, 180 for electric power, and 700 for agriculture. Industry Electric Power Water 120 Agriculture Final Demand 240 320 160 Water 480 270 Electric Power Agriculture Other Industry: 60 120 170 400 180 240 240 360 80 The output matrix is X=. (Round to two decimal places as needed.)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.
