Utility maximisation and competitive market equilibrium

The firm you work for, Coxtech, is asking you to determine which price should the company set for product x in a new location called market N, where the firm is planning to enter next year. You don’t have data available for the new market, what you have is an estimated utility function for market E where Coxtech is already operating. The estimated utility function for a tipical consumer in market E is .

Recent studies show that the preferences of consumers in market N, for goods that are similar to good x, are more sensitive in comparison to consumers in market E, where the company is already present. These estimates indicate that consumers’ valuation for products similar to x in market N are valued 20% more than what consumers in market E value them. Studies also show that in market E, even if they don’t consume the good, consumers value the fact that good x is available in the market in an equivalent of 3 utils, you can identify this in the utility function. In contrast, the studies show that in market N consumers only get satisfaction from consuming the good and they don’t get any satisfaction from the mere fact that the product is available.

Finally, both markets have the same supply function: , there are a total of 100 identical consumers in each market E and market N, and the firms are price takers.

To answer the questions below here is a summary of the information, and some questions that will help you clarify what you need to answer:

1. In market E the utility is . In market N the utility is 20% more than in market E. What is the utility function of consumers in market N?
2. Both markets face a market supply of , and there are 100 consumers in market E and 100 consumers in market N.

• In market E, if consumers consume they still get some utility, how much this is?

1. In market N if consumers get zero utility, what is different in the utility functions?

1. Obtain the marginal utilities for market E and market N. What is different in the two cases in terms of valuations for good x?

Find the equilibrium price and quantity for both market E and market N assuming perfect competitive markets and that both markets have 100 consumers each