2. Consider the following information of a hypothetical firm: Q = 100K0.6 L0.8; w = :1; r = 3 A. Solve for the cost-minimizing quantity of capital (K*) and labor (L*), and the minimum cost (C*) if the firm targets to produce 3,000 units of output. B. If target output increases to 6,000 units, solve for the new cost-minimizing quantity of capital and labor, and the minimum cost. C. Graphically illustrate the expansion path for the firm if it decides to increase its target output from 3,000 units to 6,000 units.
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- The manager of Don Teeta Company Limited hires labour (L) and rents capital equipment (K) ina very competitive market. Currently, the wage rate of labour is GH¢2 per hour and capital isrented at GH¢5 per hour, the unit price of the product is GH¢0.75 and total cost of production isGH¢1,000. Suppose the firm’s production function (Q) is as follows:? = 14?0.5?0.5 + 10Determine the optimal input usage and the maximum profit.The expansion path of a firm gives five different quantities of output such as 10,20,30,40 and 50 units; and the price of labor is $25 and the price of capital is $100 per unit. The table shows the long-run costs of the firm at given quantities of output. Q L K LTC( $) LAC( $) LMC ($) 10 64 20 3600 360 360 20 120 40 7000 350 340 30 200 58 10800 360 380 40 288 80 15200 380 440 50 440 90 20000 400 480 a. With the help of graph, analyze the properties of LAC and LMC b. Interpret and evaluate the numerical and graphical data and illustrate the relationship between LAC and LMCSuppose a firm’s total cost is C = rK + (q 2 /2K), where K = the firm’s capital (plant size), q is output and r is the price of a unit of capital. 1. What is short-run average total cost (C/q) and what is marginal cost dC/dq, assuming K is fixed at K0 (2 points) 2. Suppose K is not fixed, but output is fixed at q0. Given this exogenous output and exogenous price of capital r0, what level of capital (K*) is most efficient – that is, minimizes total cost C? Do not forget to check the second order condition (4 points) 3. Find and interpret ∂K*/∂r.
- Profit is found as total revenue (TR) minus total cost (TC). With that in mind, let us now consider the possible profits for the firm that we looked at in assignments 7 and 8, where the firm’s capital is fixed at 2 units and where the cost of capital is $40 per unit per period, while the cost of labor (or wage rate) is $30 per unit of labor per period and the firm has the following short run production function: Labor: 0 1 2 3 4 5 6 7 8 9 Output: 0 6 24 60 120 170 210 240 260 270 Now, let us further assume that the firm is perfectly competitive (i.e., it is a price taker) and that it can sell each unit of the output that it produces for $3 [remember, for price takers, the price (P) is also the marginal revenue (MR)]. (a) Use this information set up a diagram (i.e., an excel chart) that shows total cost (TC) and total Revenue (TR) of the firm per period in the short run with the level of output on the horizontal axis. (b) Also, use…RBW produces light sticks for one of their legendary girl groups, Kara. Suppose that RBWuses capital, K, and labor, L, to produce the light sticks. The production function is given as: Q(K,L)=2K0.75L0.51. Identify if RBW’s production function is increasing, constant, or decreasing returns to scale with a brief explanation. Also, solve for the company’s cost minimization problem by providing conditional demand functions of labor and capital, with respect to their input prices. Assume that w is the wage of labor and r is the rent cost of capital.2. Suppose that RBW is preparing for a mini-fan meet for the group’s “When I move” mini-album launch and that they have to provide 200 light sticks. The wage of labor, w, is $6.00 and the cost of capital, r, is $2.00. Determine how much labor and capital they have to use and the total cost of producing the light sticks.A firm has two plants that produce identical output. The cost functions are C1=346q−8q2+0.5q3 and C2=346q−10q2+1.0q3. Part 2 First, note that if AC1=346−8q+0.5q2, then dAC1dq=−8+2(0.5)q. Similarly, if AC2=346−10q+1.0q2, then dAC2dq=−10+2(1.0)q. If the firm wants to produce units of output, how much should it produce in each plant? The firm should produce _ units at the first plant and _ units at the second plant. (Enter a numeric response using an integer.) Please do fast ASAP fast
- Use second image for reference, for part b here is referene; The maximum profit is found at the tangency between the production function and the isoprofit line. In other words, the slope of the production function and the slope of the isoprofit line must be the same. This is written as MPL = w where w is the slope of the isoprofit line. Then we get sqrt1 / 2L = w => 1/2w = sqrtL => L*D = 1/4w^2A firm uses labor and machines to produce outputaccording to the production function f(L, M) = 4L1/2M1/2, where L is the number of units of laborused and M is the number of machines. The cost of labor is $40 per unit and the cost of using amachine is $10.1. Draw an isocost line for this firm, showing combinations of machines and labor that cost $400and another isocost line showing combinations that cost $200.2. Suppose that the firm wants to produce its output in the cheapest possible way. Find thenumber of machines it would use per worker. (Hint: The firm will produce at a point wherethe slope of the production isoquant equals the slope of the isocost line.)A firm has two plants that produce identical output. The cost functions are C1=346q−8q2+0.5q3 and C2=346q−10q2+1.0q3. Part 2 First, note that if AC1=346−8q+0.5q2, then dAC1dq=−8+2(0.5)q. Similarly, if AC2=346−10q+1.0q2, then dAC2dq=−10+2(1.0)q. At what output level does the average cost curve of each plant reach its minimum? The first plant reaches minimum average cost at _ units of output. (Enter a numeric response using an integer.) Please do fast ASAP fast
- A firm has the following information on production and costs from past data: Output (Y) 0 6 12 18 Total Cost (TC) 9 2775 5361 8199 If the total cost function is known to be TC=aY' + bY2 +kY + f , and the demand for the product of the firm is Y=32041/2)4, answer the following: Determine the coefficients of the cubic cost function. Derive all cost and revenue curves and the profit Show that the MC cuts the AVC when AVC is at its minimum point. Plot the relevant graph indicating all Calculate the break even and profit maximizing levels of output and price. What is the relationship between price, marginal revenue and own price elasticity of demand at the profit maximization point.rofit is found as total revenue (TR) minus total cost (TC). With that in mind, let us now consider the possible profits for the firm that we looked at in assignments 7 and 8, where the firm’s capital is fixed at 2 units and where the cost of capital is $40 per unit per period, while the cost of labor (or wage rate) is $30 per unit of labor per period and the firm has the following short run production function: Labor: 0 1 2 3 4 5 6 7 8 9 Output: 0 6 24 60 120 170 210 240 260 270 Now, let us further assume that the firm is perfectly competitive (i.e., it is a price taker) and that it can sell each unit of the output that it produces for $3 [remember, for price takers, the price (P) is also the marginal revenue (MR)]. (a) Use this information set up a diagram (i.e., an excel chart) that shows total cost (TC) and total Revenue (TR) of the firm per period in the short run with the level of output on the horizontal axis. (b) Also, use…Question Onea. The Mature Corporation produces yo-yos at its factory. Both its labor and capital markets are competitive. Wages are K12 per hour and yo-yo-making equipment (a computer controlled plastic extruding machine) rents for K4 per hour. The production function is q = 40K 0.25L 0.75, where q = boxes of yo-yos per week, K = hours of yo-yo equipment used, and L = hours of labor. i Determine the cost minimizing capital-labor ratio at this firm. ii Determine the amount of labour used in production as a function of q. b. Briefly explain factor that contribute to frictional unemployment in the economy.c. Explain why a Marginal factor cost (MFC = W) is perfectly elastic in a perfect competitive industry? d. Explain why internal markets for labor are every important for a firm?