Question

You have been hired as an economic consultant for a ski company. This company has patented a new

type of ski, and is trying to figure out how to market the new product. Complicating this is the fact that

consumer demand changes depending on the season. In this problem there are two seasons (summer and

winter). Keep in mind that in the real world, this would be expanded to 4 quarters. You will need to figure out

whether this product should be produced at all.

The only information you have available is consumer demand, which is from survey data, and production costs.

You can also assume that, because of the patent, this is a monopoly market.

Demand:

During the

winter months

, nobody is willing to pay $500 for the new skis, because there is so much

uncertainty about the new design. However, for every dollar less than $500, 1 person is willing to buy a pair.

For example: 10 people are willing to buy at a price of $490, 20 people are willing to buy at a price of $480, and

so on. The equation for winter demand is Q=500-P

During the

summer months

, even fewer people are willing to try the new skis. Nobody is willing to pay

$200, but 10 people will buy at $190, 20 will buy at $180, 30 will buy at $170, and so on. The equation for

summer demand is Q=200-P

Costs:

Lease payments for the new factory will be $20,000 per year. You can only sign leases in 1-year

periods. Variable production costs are VC=2Q^2

2

.

How many skis should be produced in the winter months? At what price should they be sold?

How many should be produced in the summer months? At what price should they be sold?

Does it make sense for this company to introduce this new ski?

(How much profit (or loss) will this new product bring?)

Answer 1