True, false or uncertain? Justify your response to the following statements. In

Question

True, false or uncertain? Justify your response to the following statements.

In class, we considered a model of market areas based on linear transportation costs and a uniform population density. For example, consider a market where the price is 20, that each consumer buys either none or one unit, that the cost of a consumer’s alternative is 30 and that the transportation cost is 5 per km. (round trip) and that total quantity demanded equals 10000.

a) If the price falls by 10 percent, how much does quantity demanded rise by?

Suppose that, contrary to class, we consider a more realistic setting where the population density is not uniform. To keep it simple enough assume that the density is triangular in the sense that the maximum density at the factory location (and equal to 50,000 people per km) and that density decreases linearly as the distance from the factory increases until, according to the local statistical bureau, density is equal to 0 at 50 km. away from the factory.  

A more realistic setting would also suppose that only a fraction of the population, < 1, actually consume the product made by the factory and that these consumers are evenly distributed amongst the population. Since the raw data on quantity demanded is the same in both cases, you need to estimate or infer .

b) Using the same information used in part a), estimate if the population density is uniform.   

c) Estimate if the population is not uniform. (Hint, remember how to compute the area of a triangle.)  

d) Comparing the two scenarios, is the price elasticity of demand for the factory higher or lower when the density is triangular?

Explanation / Answer

Assumptions : Linear transportation costs and a uniform population density

The prices and the quantity demanded are inversely proportional which means that Q2/Q1=P1/P2. Note that the prices and the quantity supplied are directly proportional. In a linear relationship, the ratio of quantity demanded and price should remain constant. Therefore, the product of 10000 and 20 should remain constant would mean that the reduction in price by 10% would result in a quantity increase of 11.11%.

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