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## Engineering Assignment Question

Q1: Consider that number of people N willing to buy cars at a given price P varies according to the

Function. N = 5000 × 2P

Note that, for example, a person willing to buy a car at a price of \$200 will also be willing to buy a car at \$100 and will be included under both. This is not a function of the number of persons with the price returned as the most they will pay.

• Provide a graph of N vs P, in an appropriate range, with N on the x axis and P on the y Be sure to appropriately label the intercepts.
• Assume we have a competitive marketplace with a total of 200 cars for sale. How much money will be spent on purchasing cars? Justify your answer.
• Now assume we instead have a monopoly. You still have 200 cars for sale. You are only allowed to sell cars at four different prices and you must sell fifty cars at each price. What is the most you can make from car sales? Justify your answer.

Q2: Consider that I have an asset worth \$2000. There are two independent threats. The first occurs with probability 0.05 and would reduce the value of the asset to \$100, while the second occurs with probability 0.01 and would completely destroy the asset. Both could occur. What would be the threshold value at which buying insurance would be “worthwhile for both parties“? Be sure to show working.

## Engineering Assignment Solution

Q1: Consider that number of people N willing to buy cars at a given price P varies according to the

Function. N = 5000 – 2P

Note that, for example, a person willing to buy a car at a price of \$200 will also be willing to buy a car at \$100 and will be included under both. This is not a function of the number of persons with the price returned as the most they will pay.

• Provide a graph of N vs P, in an appropriate range, with N on the x axis and P on the y axis. Be sure to appropriately label the intercepts.

Because there is a restriction that I cannot sell more than 50 cars at one price, the maximum price I can set would be corresponding to 50 cars i.e.

For the remaining 150 cars I can any three values as price but it should be less than \$2475. I would go with \$2474, \$2473 ad \$2472.

Total revenue = 50 x 2475 + 50 x 2474 + 50 x 2473 + 50 x 2472 = \$494700

Q2: Consider that I have an asset worth \$2000. There are two independent threats. The first occurs with probability 0.05 and would reduce the value of the asset to \$100, while the second occurs with probability 0.01 and would completely destroy the asset. Both could occur. What would be the threshold value at which buying insurance would be “worthwhile for both parties”? Be sure to show working……………..