2. Models of inventory systems frequently consider the relationships among opening stock, production quantity, demand or sales, and closing stock. For a given production period j, let Sj – 1 = closing stock from the previous period Xj = production quantity in period Dj = demand in period j Sj = closing stock for period j
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2. Models of inventory systems frequently consider the relationships among opening
stock, production quantity, demand or sales, and closing stock. For a given
production period j, let Sj – 1 = closing stock from the previous period
Xj = production quantity in period
Dj = demand in period j
Sj = closing stock for period j
Required
a) Write the mathematical relationship or model that describes how these four
variables are related.
b) What constraint should be added to produce capacity for period j is given by
cj?
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- (a) Complete the following table and draw the corresponding graphs. Capital inputs Labor inputs Total product Average product Marginal product 20 0 0 20 1 15 20 2 34 20 3 51 20 4 65 20 5 74 20 6 80 20 7 80 20 8 75 (b) What is relationship between MP and AP? Explain why MP first rises, then declines and ultimately becomes negative? (c) Whether the above phenomenon is long run or short run and why? (d) Does law of diminishing marginal returns holds in above scenario? Why and why not.A breeder tells you he has determined for each 1-lb increase in weaning weight profit increases by $1.40 per pound. However, he has also calculated that for each independent 1-lb increase in birth weight, profit decreases $5.45 per pound. 1. What would be the economic index for this aggregate breeding value? 2. If the producer gave you the following table with calf birth weight and weaning weight, what would be the index value and rank for these animals? Calf id Weaning weight Birth weight Index value Rank 608 78 589 70 566 80 532 75 5. 556 76 618 87 7. 576 74 8. 610 88 9. 595 90 10 625 73 3 4 62. An economist is interested in the variation of the price of a single product. It is observed that a high price for the product in the market attracts more suppliers. However, increasing the quantity of the product supplied tends to drive the price down. Over time, there is an interaction between the price and supply. The economist has proposed the following mode, where Pn represents the price of the product at year n, and Qn the quantity: (a) Explain the significance of the constants 500 and 100 in the proposed equation. (b) Explain the significance of the signs of the constants -0.1 and 0.2. (c) Simulate the system using the following initial conditions (plot the trajectories) and predict the long term behavior of the dynamical system. Po 100 and Qo= 500 • Po= 200 and Qo = 500 ● Po 100 and Qo = 600 Po 90 and Qo = 400 [Pn+1 = Pn -0.1 (Qn - 500) [Qn+1 =Qn +0.2 (Pn - 100) ●
- 3.cengage.com/static/nb/ui/evo/index.html?deploymentid=5981412232614779684085777463&eISBN=9780357133576&id=1498546365&sna... A < CENGAGE MINDTAP Homework(Ch 13) 5. Costs in the short run versus in the long run Ike's Bikes is a major manufacturer of bicycles. Currently, the company produces bikes using only one factory. However, it is considering expanding production to two or even three factories. The following table shows the company's short-run average total cost (SRATC) each month for various levels of production if it uses one, two, or three factories. (Note: Q equals the total quantity of bikes produced by all factories.) Number of Factories Q = 100 1 360 2 540 3 720 Q = 200 200 300 400 . Average Total Cost (Dollars per bike) Q = 300 Q = 400 240 160 160 160 160 240 Q = 500 Q = 600 400 720 300 540 200 360 Suppose Ike's Bikes is currently producing 500 bikes per month in its only factory. Its short-run average total cost is $ per bike. Suppose Ike's Bikes is expecting to produce 500…29. Consider a firm minimising the cost of production, given factor prices. For this firm, the following is observed: MPL MPK where w is the wage rate, r is the rental rate of capital, MPL is the marginal product of labour and MPx is the marginal product of capital. To minimise the cost of production, what should this firm do? a) Pay higher wages. c) Use more labour and less capital. b) Pay lower rental rate of capital. d) Use less labour and more capital.Problem 13-04 (algo) Consider the economy described by the following equations: C - 1,600 + 0.9 (Y - T) IP. 800 G. 1,600 NX 200 T 1,600 Y- 29, 000 a. Complete the table shown below to find short-run equilibrium output. Consider possible values for short-run equilibrium output as they are given in the table below. Instructions: If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers Planned aggregate expenditure (PAE) Out putY Y- PAE Y. PAE? (Click to select v (Click to select) v (Click to select (Click to select) (Click to select 27, 200 27,400 27,600 27,800 28,eee b. Short-run level of equilibrium output: c. What is the output gap for this economy? Instructions: If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. The actual unemployment rate should be rounded to two decimal places. Output gap: where Y= 29.000 If the natural rate of unemployment is 5 percent, what is the actual…
- 2. Basic Macroeconomic Model of General Equilibrium under Perfect Competition: Household faces decision about how much to consume and how much to work, it also has some capital that it rents out, max log(C) + xlog (1 - Lh) C.L s.t. C = wLh+rKh where C is consumption, L, is labour supplied by household (so 1 - L₁ is leisure), w is the wage, r is the rental rate on capital, and K is capital held/supplied by the household.¹ There is a Firm with production function Y = LK}, where Y is production, and Lf is labour used in production (demanded), and K, is captial used in production. Firms solve the profit maximization problem max Y-wL-rKf Y.Lj.Kj s.t. Y = LK- ¹Since the Household does not like capital in an of itself it will always choose to rent out all the capital it possesses. 1 note that profits equal revenues (Y, as price is normalized to one) minus costs of the inputs; labour wLf (wages paid to labour) and capital rK, (cost of renting the capital). General equilibrium will be given by…Problem 10-01 (Algorithmic) Suppose that the R&B Beverage Company has a soft drink product that shows a constant annual demand rate of 3,600 cases. A case of the soft drink costs R&B $2. Ordering costs are $22 per order and holding costs are 26% of the value of the inventory. R&B has 250 working days per year, and the lead time is 5 days. Identify the following aspects of the inventory policy: a. Economic order quantity. If required, round your answer to two decimal places. Q* 551.9 X b. Reorder point. If required, round your answer to the nearest whole number. r = 72 c. Cycle time. If required, round your answer to two decimal places. T = 38.3 X days d. Total annual cost. If required, round your answer to two decimal places. TC = $2.11 A company wants to develop a level production plan for a family of products. The open- ing inventory is 100 units, and an increase to 130 units is expected by the end of the plan. The demand for each month is given in what follows. Calculate the total production, daily production, and production and ending inventory for each month. Month May Jun Jul Aug Total Working Days 21 19 20 10 Forecast Demand 115 125 140 150 Planned Production Planned Inventory 100
- 5. Suppose the production function is given by f(E, K) = E'/³K²/3. The hourly wage rate is $2 and the price for a unit of capital is $32. The output level is ĝ = 144 and the price of the output is $30. (a) Write a firm's CMIN problem. (b) Impose FONC to find MP(E) = w and MP(K) = r. %3DDescribe the results shown in the following graph. 1) What does Estimated Effect mean here? 2) What do the authors find? 3) Why is the estimated effect near O for 4 months after the implementation of a stay at home order? 12 Months from stay home order Estimated EffectRecall the production modelMax 10x s.t 5x < 40 x > 0 Suppose the firm in this example considers a second product that has a unit profit of $5 andrequires 2 hours of production time for each unit produced. Use y as the number of units ofproduct 2 produced.1. Show the mathematical model when both products are considered simultaneously.2. Identify the controllable and uncontrollable inputs for this model.3. Draw the flowchart of the input–output process for this model 4. What are the optimal solution values of x and y?5. Is the model developed in part (a) a deterministic or a stochastic model? Explain