People are often amazed at the quality of produce that is available in markets far away from where that produce is grown-and that it is often the case that the average quality of produce is higher the farther the place where the produce originates. Here we will try to explain this as the result of producers' awareness of relative demand differences resulting from substitution effects.
A: Suppose you own an apple orchard that produces two types of apples: High quality apples x1 and low quality apples x2. The market price for a pound of high quality apples is higher than that for a pound of low quality apples-i.e. p1 > p2. You sell some of your apples locally and you ship the rest to be sold in a different market. It costs you an amount c per pound of apples to get apples to that market.
(a) Begin with a graph of a consumer who chooses between high and low quality apples in the local store in your town. Illustrate the consumer's budget and optimal choice.
(b) The only way you are willing to ship apples to a far-away market is if you can get as much for those apples as you can get in your town - which means you will add the per-pound transportation cost c to the price you charge for your apples. How will the slope of the budget constraint for the far-away consumer differ from that for your local consumer, and what does that imply for the opportunity cost of good apples in terms of bad apples?
(c) Apples represent a relatively small expenditure category for most consumers-which means that income effects are probably very small. In light of that, you may assume that the amount of income devoted to apple consumption is always an amount that gets the consumer to the same indifference curve in the "slice" of tastes that hold all goods other than x1 and x2 fixed. Can you determine where consumer demand for high quality apples is likely to be larger - in the home market or in the far-away market?
(d) Explain how, in the presence of transportation costs, one would generally expect the phenomenon of finding a larger share of high quality products in markets that are far from the production source than in markets that are close.
B: Suppose that we model our consumers’ tastes as u(x1,x2) = xα1 x2(1−α).
(a) What has to be true about α in order for x1 to be the good apples.
(b) Letting consumer income devoted to apple consumption be given by I, derive the consumer’s demand for good and bad apples as a function of p1, p2, I and c. (Recall that c is the per pound transportation cost that is added to the price of apples).
(c) What is the ratio of demand for x1 over x2?
(d) Can you tell from this in which market there will be greater relative demand for good versus bad apples—the local market or the far-away market?
(e) In part A, we held the consumer's indifference curve in the graph fixed and argued that it is reasonable to approximate the consumer's behavior this way given that apple expenditures are typically a small fraction of a consumer's budget. Can you explain how what you just did in part B is different? Is it necessarily the case that consumers in far-away places will consume more high quality apples than consumers (with the same tastes) in local markets? Can we still conclude that far-away markets will have a higher fraction of high quality apples?