Given the following cost function, determine the underlying production function. 1 2C(m, w, y) = 10mwy, where y is the output and m and w, are the prices of two inputs x1 and x2 respectively
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Given the following cost function, determine the underlying production function.
1 2C(m, w, y) = 10mwy, where y is the output and m and w, are the prices of two inputs x1 and x2 respectively.
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- Consider the production function: Y = 0.75X + 0.0042X2 – 0.000023X3 If input price is 0.15$ and output price is 4$ then at what level of X, profit will be maximum?(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.b Now suppose Q = 2L +3K. Let the market price of L be w = 5 and the price of K be r = 4. Let both L and K can vary with production. Compute the input demand functions as a function of Q. (4 Points) c Calculate the marginal cost and average cost of the above function in subpart (b). Show them graphically. At what prices of textile will the producer shut down production. (3 Points) d Now suppose Q = 10LK. The market prices of inputs are as in subpart (b) above. Compute the input demand functions as a function of Q. Find the optimal production when the price of textile is $10 per yarn. (5 Points)
- 1. Find the cost minimizing input demand functions (x¿(w,q)) and the cost function (c(w,q)) for the following production functions: 1/3 21382 a. f(x) = x₁Find the marginal values for functions a, b, and c given below and evaluate each at Q=100. a) C(Q) = 540 + 6Q where C(Q) is the total cost function and Q is the level of production. b) R(Q) = 9Q where R(Q) is the total revenue when Q units are transacted at a constant price of P=$9. c) R(Q) = P(Q)Q, where P(Q) = 40 – 0.1Q, is a demand (inverse) function showing the dependence of price on quantity demanded Q.1. Let input prices be (wK, WL) and output price be p. The production function is given by f (K, L) = min [√K, L]. (b) Derive the cost function. Use the cost function to derive the output supply function.
- A commodity has a demand function modeled by p= 100-0.5x and the total cost function is C= 50x+37.5 if x is number of units. Price of maximum profit has to be calculated. We have to find the price where there is the maximum profit.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 price-demand equation and the cost function for the production of active styluses are given, respectively by p = 470 -0.05x and C(x) = 160,000 + 22x d) Given a price of $150, determine whether the price should be increased or decreased in order to increase revenue. e) Find the revenue function, R(x). f) Calculate the number of styluses the company should sell in order to maximize revenue. g) Find the approximate cost of producing the 140th stylus.
- 2) Assume a firm has the following production function: 1 = K³L3¸ Assume w= 2, v = 16 and that K = 27 in the short run Further assume the firm faces a market price of 32. a) What is the firm's level of production and labor that can maximize the profit in the short run? b) If you were their economic consultant, what would you advise them to do regarding short run production and future adjustments to K and L? Explain1. If the cost function of producing a commodity is: 40 + 50x + Vx2 +1 10 C (x) = = where x represents the number of units produced. Calculate the marginal cost of producing 20 units.Given the production function f(x,x2) x,ax,, calculate the profit maximizing demand and supply functions, and the profit function. ii. %3D