A soda bottling plant uses are capital (K), electricity (E) and raw materials (R) in production. Its production technology can be represented by the following function: Q(R, E, K) = R1/3 E²/3 + K where, Q is the number of bottles produced. The capital used in production is fixed at any point in time because it uses a fully automating assembly line production. The plant can only vary the quantity of raw materials and electricity to adjust output or costs. The hourly cost of raw materials (p) is $10 and the hourly rate of energy (h) is $12. The total hourly cost of capital is $100. The marginal productivities of R and E are as follows: 1 MPR =R-2/3 E²/3 , MPE = 2R/³E-1/3 R/3E-1/3 vi) What is the maximum hourly output the plant can produce if K=30? A.) Q= 10.06 B.) Q= 7.02 C.) Q= 37.02 D.) Q= 17.67

A soda bottling plant uses are capital (K), electricity (E) and raw materials (R) in production. Its production technology can be represented by the following function: Q(R, E, K) = R1/3 E²/3 + K where, Q is the number of bottles produced. The capital used in production is fixed at any point in time because it uses a fully automating assembly line production. The plant can only vary the quantity of raw materials and electricity to adjust output or costs. The hourly cost of raw materials (p) is $10 and the hourly rate of energy (h) is $12. The total hourly cost of capital is $100. The marginal productivities of R and E are as follows: 1 MPR =R-2/3 E²/3 , MPE = 2R/³E-1/3 R/3E-1/3 vi) What is the maximum hourly output the plant can produce if K=30? A.) Q= 10.06 B.) Q= 7.02 C.) Q= 37.02 D.) Q= 17.67

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter8: Cost Analysis

Section: Chapter Questions

Problem 5E

See similar textbooks

Similar questions

Let f(x1,x2)=xxx be a Cobb-Douglas production technology where a, ẞ> 0 and a+B< 1. (i) Show that the technology satisfies monotonicity, diminishing marginal product, diminishing TRS, and diminishing returns to scale. (ii) Which of these properties are invariant to arbitrary increasing transfor- mations of the technology? That is, which properties remain true for oof(x1, x2), where can be any strictly increasing function? You can assume that is differentiable for convenience. 2. Solve for the short-run profit maximization problem for f(x1, x2) = 2x1 + x2 and f(x1, x2) = min{2x1, x2}, holding x2 at 2, and taking real factor prices wi and w2 as given.
Assume you were hired as a Production Engineer in a global Bearing Manufacturer company and given the following inputs: Equipment Maintenance Cost per Month Utilities Cost per Month Material Cost per Unit Labor Cost per Unit Selling Price per Unit S60,000.00 $12.000.00 $12.00 $3.00 $24.00 Calculate Total Fixed Cost per Month Calculate Total Variable Cost per Unit = Calculate number of Units to be sold to reach Break-Even Point = Calculate number of Units that must be sold to eam profit of $90,000.00
Consider a power system with three generators. Each generator has a piecewise linear cost function defined by the following points. Generator 1 Generator 2 Generator 3 Production (MWh) 100 200 300 400 200 400 600 800 100 400 700 1000 Cost ($) 915 1760 2635 3540 1870 3530 5230 6970 1060 3460 6040 8800 The min/max production of each generator corresponds to the min/max production values in the table (i.e., Generator 1 produces at least 100 MWh and no more than 400 MWh). (a) Plot the inverse supply function for this system. (b) If the demand is completely inelastic and equal to 1600 MWh į. compute the electricity price. ii. calculate the gross consumer surplus, consumer surplus, the producers revenue, the producers profit, and the global welfare. iii. determine the production level, cost, revenue, and profit for each generator.
Suppose that the production function takes the form X = min(10L, 5K) and that a competitive firm faces a wage rate of £60 per week and a weekly capital rental of £32. (a) How much must the firm spend to produce 100 units of output, and what is the average cost of production when X = 100? (b) What is the incremental cost of producing the 101st unit of output? (c) What happens to the cost of producing 100 units of output if the wage rate and the rental cost of capital rise by 25 per cent each? What happens to the average and marginal cost? (d) What happens to the cost of producing 100 units of output if the wage rate increases by £1, or if the cost of capital increases by £1?
Assume that it costs a company approximately C(x) = 400,000 + 140x + 0.003x? dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. 400,000 – 0.000009 Use it to estimate how fast the cost is increasing when x = 10,000. 2$ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) = C(10,000) = $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. -Select--- at a production level of 10,000 smartphones. The marginal cost from (a) is --Select--- than the average cost from (b). This means that the average cost is
1. For each of the cost functions given below, do the following things: C(T) = = 10 + 2T. C(T) = T0.8 (a) Draw the graph for C(T), with T on the horizontal axis. Explicitly the values for the intercepts. (b) Derive AC and MC respectively, and draw their curves. (c) Determine whether the cost function exhibits IRTS or DRTS or CRTS.
Price and cost ($ per 1,000-gallon unit) Return t A municipal water utility employs quasi-fixed capital inputs-the water treatment plant and distribution lines to homes-to supply water to 20,000 households in the community it serves. The figure below shows the cost structure of this utility for various levels of water service. Quantity of water consumption is measured in 1,000-gallon units per month. AQFC is the average quasi-fixed cost curve, and LAC is long-run average cost. Long-run marginal cost, LMC, is constant and equal to $4 per 1,000-gallon unit. The inverse demand equation is P= 24 -0.0004Qd 10 14 MR Quantity (1,000-gallon units per month) Quasi-fixed capital inputs cost per month is $ LAC AQFC LMC D
A Iqbal production function takes the form: Q = min [5L, 6K]. What are the optimum values for L and K to produce an output level (Q) of 30 units? A. L = 6 and K = 0 B. K = 5 and L = 0 C. K = 5 and L = 6 D. Answer cannot be established without knowing the cost of L and K inputs
(b) A firm has an average cost function 125 q? 4. 16 A(q) %3D - where q is the firm's output. (i) Determine the level of output for average costs are minimum. (ii) Hence determine the range of values for which average costs are decreasing. (iii) What part of the decreasing range is practically feasible?
Q) Economies of Scale What will happen to the cost of producing Teslas if the Shanghai gigafactory doesn’t achieve economies of scale?
With the table started as indicated below, calculate the cell indicated as an Qx stands for quantity (units) of variable input (for instance, units of an equipment) Px = price of the variable input = $3000/unit Price of output is $150 per unit TFC is assumed to be = 7,500 (e.g. leasing an office space) %3D Qx TPP MPP APP TVC TC AVC ATC TR MRP MC MR 0 0 1 2 50 30 50 36 6 200 8 -20 20 3. 4. 7,
Q4 The output of a production process, Q, is given by the function KL Q = K+ 2L where K and L denote capital and labor. (a) Calculate the output when the capital and labor are 40 and 30 units, respectively. (b) Find the level of labor needed to produce 4 units of output when 10 units of capital are used. (c) Transpose this formula to express K in terms of Q and L. Q5 3 The equations defining a simple model of the economy are: C = 0.75Y + 18 I = 22 where C, Y and I denote consumption, national income and planned investment, respectively. Use this model to complete the following table of values and hence draw an accurate graph of C + I plotted against Y on the interval 0 < Y< 200. 100 200 C + I By drawing a second line on the diagram, calculate the equilibrium level of national income. Use your graph to explain what happens to the equilibrium level of national income when the marginal propensity to consume decreases with autonomous consumption fixed.