Reference no: EM1313179

You have been hired as a plant manager for a firm that produces widgets (Q) in Angola, Indiana. Widget production requires machine time (K) and labor time (L). The factory works three eight-hour shifts each day. Below is input and output data from the last twenty-one shifts:

Shift	Widgets	Machine Hours	Labor Hours
1	4067	2540	1029
2	4313	2786	1042
3	4493	2757	1165
4	4503	2397	1421
5	4066	2754	920
6	4641	2364	1556
7	3929	2604	916
8	4222	2530	1131
9	4272	2852	986
10	4728	2637	1399
11	4310	2724	1073
12	3980	2430	1039
13	5011	2773	1499
14	4495	2492	1341
15	3971	2433	1032
16	4597	2652	1298
17	4662	2392	1548
18	4533	2296	1532
19	4400	2722	1128
20	4392	2829	1065
21	4715	2511	1487

1. Your engineers tell you that the marginal product of both labor and machine time diminishes as the volume of production expands during any one shift. What is your production function? You should round all parameters to exactly two decimal places.The chief operating officer of the company asks you to meet a production goal of 4800 widgets during the next shift.

2. In a table, calculate how many machine hours are required to meet the Q = 4800 production goal if L=300, L=400, L=500, L=600, L=700, L=800, L=900, and L=1000.  Graph the isoquant that these calculations imply.  Explain in very clear and complete terms why the isoquant has the shape that you observe.

3. The unit depreciation expense of one machine hour is $130 and the expense of one labor hour is $65.  What combination of machine and labor hours minimizes the cost of producing 4800 widgets?  Do you believe that the firm should make production at Angola more or less capital intensive?  Explain your reasoning in full detail.

4. The firm is considering a movement of the plant to Shenzen, China where labor is cheaper.  The same mathematical relationship between inputs and outputs will hold.  A new plant in Shenzen would enjoy a one hour expense for labor of $40.  Because of a scarcity of modern equipment, the expense of one machine hour would jump to $320.  Can the move to China be financially justified?  Theoretically, how will the mix of inputs in Shenzen compare to the mix of inputs in Angola? 

For political reasons, the plant is not moved to China.  You receive news that certain machinery is unavailable for the foreseeable future.  Due to unscheduled changeover work, use of machinery is constrained to 1500 hours each shift.  This news comes at a bad time.  The COO tells you that market demand for output has dramatically grown.  The equilibrium price for a widget has risen to $160.

5. You are told to produce a quantity that maximizes profit. How many units do you produce and what is your profit?  How many machine and labor hours are used in production.

6. At this level of profit-maximizing output, what is your marginal cost, average variable cost, and average fixed cost of production?

7. The COO notifies all plant managers in the company of a simplified bonus program.  A plant manager's bonus will be tied to one measurement - average production cost.  The lower a plant's average production cost, the higher the bonus.  Is this type of bonus structure in the interest of the company?  Use theoretical and graphical insights from chapter five of the textbook to explain your reasoning.