Question

Tutorial IU Chapter 21 - Cost Minimization Chapter 22 - Cost Curves 1. A firm has the production function f (*1, 12) = . Let the price it pays per unit of input 1 bew, and the price it pays per unit of input 2 bet. (a) Find the firm's conditional input demand functions. (b) Find the firm's total (long-run) cost function. (c) How your solution would change if this firm is working in short-run and value of factor 2 is fixed at is? 2. A firm has the production function f(21,1) = (v11+3/73). The price of input 1 is y = $1 and the price of input 2 is = $1. (a) Find the firm's conditional input demand functions. (b) Find the cheapest way to produce 160 units of output. What is the firm's total cost? 3. A firm has the production function f(11,12)= min (3.r, 23). Let the price it pays per unit of input l be t, and the price it pays per unit of input 2 bewy. (a) Use a graph to draw isoquants to present the production of 12 and 24 units of output. (b) Does this technology exhibit constant, increasing or decreasing returns to scale? (c) If w y 26, what is the lowest possible cost to produce 12 units of output? (d) Write a function to represent the costs of producing 12 units of output for any input prices and 4. A firm has the total cost function CG) = y +4. (a) Find the equations for its fixed cost, average fixed cost, variable cost, average variable coverage total cost and manal cost (b) Present the average variable cont, average total cost and marginal cost functions on a graph (e) Find the minimum value for the average variable cost and average total cost. IBOBQBOTH

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Answer 1

1. The production functions is given by flow, des) = Persea Price of a wi/ unit and a Price of ses a we/ unit E. Fisms try to minimise their cost by optimally choosing inputs glawr a given amount of wei output. 10) Mim wise + Wal subject to q = No to . The Lagrange equation is : L = wish + wala ta [- dexo] Foes out on a W1 - 9:12 CO 3 w52 0 . e we as whole.. eta I - vakso => 42,892 Q -.... from ☺ @ we get, from 6, na vs. 2 > n = z and see = qdor. These are the conditional demand function to produce ē units of output. Firm's total cost is given by wint who la To preddo produce a units of outpert, fierung input demand is , du = q he es = q no Hance firms total cost functian is given by : C(9) = .2 met gt wezi uver = aq duren

( Now H = in shart-aun, minimise wist we 22 . subject to irms a zda se 09, šte = a? - Minnes4 to 2 g ] Rom Ve Foco nos * + w2.2. 2o. 7 minutter og 2 >> m 23 -0. I en av en a shart-sinn east functiam sq) = we set uz kr Bis zaffa helyett ny ão 2 % dureribs + bez mene i 3 de
​​​​​​I have done the first question(all three parts). Firms can choose inputs optimally to minimise given output. This minimisation exercise gives us the firm's input demand for given output. From the conditional input demand we can get the cost function. For short run, one input is fixed at a given value. Then firms optimally choose the other input to minimise the cost and then we get the short run cost function of the firm.