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In 2012, the box industry was perfectly competitive. The lowest point on the

long-run average cost curve of each of the identical box producers was $4, and

this minimum point occurred at an output of 1,000 boxes per month. The

market demand curve for boxes was QD = 140,000 – 10,000Pwhere P was the price of a box (in dollars per box) and QD was the quantity of boxes demanded per month. The market supply curve for boxes was QS = 80,000 + 5,000P where QS was the quantity of boxes supplied per month.

a. What was the equilibrium price of a box? Is this the long-run equilibrium price?

b. How many firms are in this industry when it is in long-run equilibrium?

 

 
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Your instructor can suspend a 30-foot rope approximately 2 feet off the ground. You and the rest of the class should get on one side of the rope. The rope represents an electrified fence, and your task is to get everyone successfully over the rope without touching it. You may not touch, lower, raise, or adjust the rope in any manner. You may not let any part of your skin or clothing touch the rope, nor can you drape anything over the rope to protect you from the “current.” There are two rules you must follow to successfully navigate the rope. First, before starting to cross the rope, everyone in the group must form a line parallel to the rope and hold hands with the people on either side. These links with the other people in the group cannot be broken. Second, a quality error is committed if any group member touches the rope. If the group detects their own error, then only the person currently attempting to navigate the rope needs to start over. If the instructor catches the error but the group does not, then the instructor can have the entire group start over. This is analogous to catching a bad product before it is delivered to a customer instead of delivering defective products to customers. You will have about 25 minutes to plan and execute this exercise. After the exercise your group should discuss the role of personality traits as well as analytic, practical, creative, and emotional intelligence in the exercise.

 

 
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The long-run supply curve for a particular type of kitchen knife is a horizontal

line at a price of $3 per knife. The demand curve for such a kitchen

knife is QD = 50 – 2P where QD is the quantity of knives demanded (in millions per year) and P is

the price per knife (in dollars). What is the equilibrium output of such knives?

b. If a tax of $1 is imposed on each knife, what is the equilibrium output

of such knives? (Assume the tax is collected by the government from the

suppliers of knives.) c. After the tax is imposed, you buy such a knife for $3.75. Is this the longrun

equilibrium price?

 

 
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Integer Programming Models.

Glueco produces two types of glue on three different production lines. Each line can be utilized by up to 7 workers at a time. Workers are paid $600 per week on production line 1, $800 per week on production line 2, and $1000 per week on production line 3. A week of production costs $1000 to set up production line 1, $1500 to set up production line 2, and $2000 to set up production line 3. During a week, on production line 1, each worker produces 20 units of glue 1 and 25 units of glue 2; on production line 2, each worker produces 30 units of glue 1 and 30 units of glue 2; on production line 3, each worker produces, 50 units of glue 1 and 35 units of glue 2. Each week, at least 120 units of glue 1 and at least 150 units of glue 2 must be produced. Formulate an IP to minimize the total cost of meeting weekly demands.
4.1) Following the 5 steps introduced in class, model the above problem. Do not solve.
4.2) (Please add the following requirement after modeling, you do not need to write the whole model again) Instead of using any combination of production lines, you can use at most two production lines.

 
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