8. A firm's total cost function is given by TC = 3Q} +2Q,Q, +7Q; Where Q, and Q, denote the number of items of goods 1 and 2, respectively that are produced. Using the substitution method, find the values of Q, and Q, which minimize costs if the firm is committed to producing 40 goods of either type in total.
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- 2 The prices of inputs x1; x2; x3; x4 are p1 = 2; p2 = 2; p3 = 5; and p4 = 2. If the production function is given by f(x1, x2, x3, x4) = min{x1, x2} + min{x3, x4}, what is the minimum cost of producing one unit of output?.A firm has the production function F(L, K) = L^1/2 + K^1/2The price of labor is $10 and the price of capital is $15. The firm has a production goal of Q = 100 units ofoutput.a) Neatly specify this firm’s cost minimization problem, using the particulars associated with this problem.b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of thisproblem.c) Solve the two equations for the firm’s optimal choice. Show your work.Q5 A firm's production function is Q is equal to 5L2Ka) Find out the MPL and MPb) Does this production function exhibit constant, increasing, or decreasingreturns to scale?c) What is the marginal rate of technical substitution of L for K for thisproduction function Q6.Suppose the firm sells its output according to the following demand scheduleMarginalTotal Product Total Revenue eLabor Product Price Revenue Product$3.50192c2.80182.30291.80391.65471.5021.4053Fill in the remaining two columns of the table. How many workers wilhired at a wage of $72
- The weekly revenue from the sale of a product is increasing at a rate of \$10$10 per \$1$1 increase in price, and the price is decreasing at a rate of \$0.5$0.5 per additional product sold. What is the marginal weekly revenue with respect to the number of products sold? Interpret your answer and be sure to state the units.Gıven two inputs X1 and X2 with Prices W1 and W2, and a production function Y=F(X1X2) show that the marginal rate of substitution between the two inputs is equal to the ratio of their prices.Suppose that the production function for a phone is ? = 20K^0.5L ^0.5 . The marginal product of labor is 10(k/l)^0.5 , and the marginal product of capital is 10(L/K) ^0.5 . Suppose that labor can be hired for $6 and capital can be hired for $9. a. When the firm is producing 49 units at lowest cost, what will the firm’s marginal rate of technical substitution be? b. Solve for the lowest-cost combination of labor and capital that will allow the firm to produce 49 phones. Fractional units of labor and capital are allowed. c. What is the minimum cost of producing 49 phones?
- Suppose that a firm has production function F(L, K) = L2/3 K1/3 for producing widgets, thewage rate for labor is w = $400, and the rental rate of capital is r = $25.d) Determine this firm’s minimum cost of producing 120 units.e) Now suppose that the firm’s production goal is left as the variable Q. Come up with the firm’s costfunction C(Q). Show your work.Suppose the utility function of a person consuming two commodities X and Y with income Birr 600 is given by U =2xy. If the per unit price of X is Birr 20 and per unit price of Y is Birr 40. a) Calculate the utility maximizing level of consumption of X1 and X2. b) Find the MRSX, Y at the optimum.If the production function of a firm is given by Q=,and the input prices are r = Birr 8 per unit and w = Birr 2 per unit,Given a Cobb-Douglas Technology specified as follows:f(x1, x2) = x1α x21−α 1. Find the marginal rate of technical substitution (MRTS)2. Derive the expression for Elasticity of Substitution
- A firm has a linear demand function for its product. When the price of the product isSh.220, the quantity demanded is 40 units. When the price increases to Sh.240, thequantity demanded becomes 30 units. In addition, the firm’s marginal cost function isgiven by:MC = 40q – 2q2 + 2Fixed cost = Sh.5 millionWhere q = quantity demanded, MC = marginal cost (Sh. million)Evaluate the level of output that maximizes profits.Homework 2.1 Suppose a business manager of the factory wants to assess in terms of elasticity of demand, whetherthe products that his business is producing are complement goods or substitute goods inconsumption. So please explain which are the factors need to consider the long-run average cost curve in terms of usage of input?Define Cobb-Douglas production. How does the elasticity of substitution (assume sigma = 1) between two inputs affect the shape of a single ISOQUANT? Use a diagram to support your answer.