Question 1 [15 points]
a.Is buying a 1-liter laundry detergent bottle for $6 when there are ½ liter bottles of the same detergent available for $2.50 each necessarily irrational? Explain your answer.[7 points, reasoning must be correct for full credit]
b.Mary and Bob consume only wine () and cheese (). Mary’s utility fromandcan be expressed as. Bob’s utility fromandcan be expressed as. Do Mary and Bob have the same preferences for wine and cheese?Explain your answer.[8 points, reasoning must be correct for full credit]
Question 2 [40 points]
Jack consumes only food () and Uber rides (). His utility function isHe lives in New York City (with his parents, so he doesn’t have to pay rent!), where food costs $4 per unit, and Uber rides cost $20 each.His budget for these two goods is $4000 per month.
a.Find the optimal amount of food and Uber rides for Jack to consume each month. Call these amountsand.[10 points]
b.The local government decides to regulate food prices to help New Yorkers. Food is nowper unit. Find the optimal amount of food and Uber rides for Jack to consume each month now. Explain why the optimal amounts changed, if applicable. Is food a complement to or a substitute for Uber rides? Explain.[10 points]
c.For the local government to pay food producers for the reduced price of food, it will have to impose a tax on New York residents. Suppose the total tax amount is based on the new price difference times the amount of food Jack previously consumed:. This amount will be subtracted from Jack’s total budget of $4,000. How much food and Uber rides will Jack consume per month now? Call these amountsand.[7 points]
d.Is Jack better off in part (c) relative to part (a)? Explain how you arrived at your conclusion.[3 points]
e.Producers complain that the government hasn’t compensated them sufficiently for lost profits because Jack responded to the price decrease by buying more food than before. They demand to be paid. If the government implements this transfer and taxes Jack accordingly (by subtractingfrom his budget constraint), how much food and Uber rides will he consume? Will he be better or worse off than in part (a)? Explain how you arrived at your conclusion.[10 points]
[NOTE:we are ignoring the producer side here, so this analysis is necessarily incomplete. We will study price regulation in more detail when we talk about markets!]
Question 3 [20 points]
Jill buys only chocolate and wine. Her annual demand function for chocolate is:
whereis the quantity of chocolate demanded,is the price of a bar of chocolate,is the price of a bottle of wine, andis Jill’s wealth.
a.Is wine a substitute or complement for chocolate?[3 points]
b.Is chocolate a normal or inferior good?[3 points]
c.If, compute the own-price elasticity of demand for chocolate and state whether it is elastic or inelastic.[6 points]
d.Using the same parameters, compute the cross-price elasticity of the demand for chocolate with respect to the price of wine.[4 points]
e.Using the same parameters, compute the income elasticity of the demand for chocolate.
[4 points]
Question 4 [25 points]
Pick a publicly traded company (other than Facebook) and answer the following questions about its likely customers. Explain your answers briefly. I am mostly looking for thoughtful answers that apply the principles we learned in class. You do not need to spend hours researching the company. Your answers should be about a page long.
a.What is/are the company’s main product(s)from which it derives profits/revenue?[5 points](Be careful here. For example, Facebook’s “products” are actually its users, not its website, because its revenue stems from advertising.)
b.Who are the company’s paying customers?[5 points](For Facebook, this would be other companies that buy Facebook ads)
c.What are some things that affect these customers’ demand for the product(s)?[5 points](For Facebook, this would be things like general economic conditions, the price of the ads, and the effectiveness of the ads in raising the company’s sales, which could depend on how many users are actively using Facebook.)
d.Is demand for the product(s) likely to be very inelastic, very elastic, or moderately elastic with respect to the price of the product?[5 points](At this point, I did some brief internet research, e.g.,this article. The price of Facebook ads has been rising and the number of ads has been rising as well. Note that this doesnotmean Facebook ads are a Giffen good – the increase in prices is surely at least part demand-driven. However, it does suggest that demand for Facebook ads is fairly inelastic; if it were very elastic, raising prices would be very difficult in any circumstance.)
e.How do you think demand would respond to rising/falling incomes of consumersand/orthe company’s paying customers (if these are not consumers)?[5 points](If incomes of Facebook users fall, demand for Facebook ads would fall as well. Likewise, if corporations’ incomes fall, their advertising budgets would likely shrink, reducing the demand for Facebook ads.)