1. Question. What would be the change in quantity demanded from the 20 percent increase in the price of American Express Cards? Was the increase a good move on the part of American Express? Should American Express increase its price more, or decrease the price of cards? Explain.
From our data, revenues for American Express increased by about $65 million dollars, which is 5.9 percent. The 10 dollar change is 20 percent of a price of 50 (weighted average price of Gold and Green cards) so we need to divide 5.9 by 20. Thus
5.9/20 = .295 = 1 + ep
or ep= -.705. We find that a 20 percent increase in the price of American Express Cards lowers quantity demanded by 14.1%, or by about 2.81 million cards. We know total revenue went up, and since quantity went down, the firm likely increased profits (total cost should fall if quantity falls). In fact, since elasticity is still below 1 in magnitude, AMEX should increase price again.
2. Question. If you were in charge of the budget for New York City in 1990, would you lower the tipping fee? Explain. (HINT: What would happen to revenue collected?)
First, think about the demand elasticity. Is it elastic or inelastic?
Clearly, something smells here (excuse the pun). Using the figures in the article, 10000 tons (the decrease in 1988) is 25% to 30% of about 33000 tons per day. At the old price of $18.50, the landfill took in about $610500 per day in revenue. When the price was increased to $40 per ton, intake fell to 23000 tons, but total revenues were 40 x 23000, or $920000 per day. Dropping the price back to $25 would bring an additional 3500 tons per day, or a total of 26500, with revenues of $662500. Lowering the tipping fees now would cost the city over $300000 per day.
(This paragraph is not part of the answer I expect) So, where did the $20 million figure come from? Here are two possible scenarios. The difference between $662500 and $610500 is $52000 per day. Multiplied by 365 gives $18.98 million, close enough to $20 million. The department figured the gain on the old ($18.50) price, not the new ($40.00) one. Alternatively, 3500 multiplied by $25 equals $87,500 per day. Multiplied by 250 work days per year gives $21.88 million. Of course this approach ignores that all garbage would get the lower price, not just the additional 3500 tons per day. If the department had paid attention to demand curves and elasticities, their policy making would be better.
3. Question. Does the rectangle PrabPe measure the total welfare loss? What other welfare losses are there from the peanut quota?
It does not include the consumer surplus lost to dead-weight loss, triangle abc. Moreover, this transfer to peanut farmers and quota holders is in real prices, not the consumer's surplus lost.
Quota holders were either growing peanuts back when the program first started four decades ago, or bought them or inherited them from original quota recipients. More than a third of the 44,000 quota holders rent them to other farmers rather than grow peanuts themselves. And they are hard to get. Some counties in Georgia make it illegal to sell quotas out of the county. Nobody grows (quota) peanuts in Maryland or Kansas because there are no quota holders there. Georgia, with 15000 peanut farmers holding quotas for 1.3 billion pounds (41% of the total allotment), is the largest peanut growing state. Alabama and Texas also have a lot of the quota. California, which could grow a lot of peanuts if allowed, has only two peanut quotas.
So a lot of non-quota holding farmers lose. In the figure Qe units of peanuts would be grown in a free market. The quotas restrict that to Qr, and the growers forced out by not having quotas lose bcd worth of surplus value. The net result is a huge transfer to quota farmers as the expense of consumers and other potential peanut farmers.
4. Question. How do price controls effect consumer and producer surplus. You might need draw a graph of the market with and without price controls to answer this question.
When the supply curve shifted in from S1 to S2, without price controls the price would increase to P2. Consumer surplus = the areas (a+b+c) and producer surplus = the areas (d+e+f). But if the price is controlled at P1, the real price (in terms of time, etc.) will rise to P3 since only Q3 units of gasoline will be provided,a nd in that case demand sets the price. Consumer surplus falls to the area (a) while producer surplus is the areas (f+e+b). Sellers may gain or lose surplus, depending on the sizes of areas d and b. There is a dead weight loss of areas (c+d).
5. Question. Why were customers treated unfairly by Chrysler's decision? After all, is a payment to the seller equivalent to a payment to a buyer?
The figure shows why you could argue
Chrysler was unfair. Before the dealer incentive plan, Chrysler dealers had a supply
curve of S. Implementing the plan shifts the shadow supply curve down to Dg,
and the new equilibrium occurs at a quantity of Qg. Consumers pay only Pc
while dealers get Ps, the difference being paid by Chrysler Corporation. If
instead the money was given directly to customers in the form a rebate, the supply curve
would remain as S, but there would be a shift of a shadow demand curve to Dg.
But the result is the same quantity, and buyer and seller prices as under the dealer
incentive plan. And this would hold with any set of supply and demand curves, because the
equilibrium is determined where Ps and Pc differ by the subsidy,
which occurs only at the quantity Qg.
TECHNICAL PROBLEMS
1. Suppose you face the following demand curve for you product: Q = 1500 - 30P.
a) Find the elasticity of demand if the price changes from 10 to 11.
ep=% change in Q/% change in P. At P=10, Q=1200. At P=11, Q=1170. % change in Q=(-30/1200)x100=-2.5%. % change in P=10%. Thus, ep=2.5/10=0.25.
IF YOU USED THE POINT ESTIMATE FOR ELASTICITY IN THESE QUESTIONS [ie., ep=(changeQ/changeP)*(P/Q) with the fact that (changeQ/changeP)= -30] YOU GET FULL CREDIT, AS LONG AS YOU SHOWED YOUR WORK.
b) Find the elasticity of demand if the price changes from 15 to 16.
P=15 means Q=1050. P=16 means Q=1020. % change in Q=2.86%. % change in P=6.67%. ep=.428.
c) What happens to the elasticity of demand as price goes up? Figure out at what output the price elasticity of demand is unit elastic.
As the price goes up, the elasticity gets larger. You can find the unit elastic output by trial and error, but it will be at Q=750. Whenever you have a linear demand function, unit elastic occurs at 1/2 the Q intercept.
2. Suppose the demand for gasoline is given by Qd = 50 - 0.5P and the supply by Qs = 0.2P - 6. If Locke proposes a 20 cents a gallon tax increase, answer the following:
a) What is the equilibrium quantity and price before the tax increase (pretend the initial tax is zero)?
Set Qd=Qs, so 50-0.5P=0.2P-6. Solving for P we find P=80 (alright, so I'm still living in the 1970s). When P=80, Q=10.
b) What is the consumer surplus before the tax? What about the producer surplus?
You can use the area of a triangle rule here. Looking at the graph, the consumer surplus triangle area = 0.5*(100-80)*10=100. The producer surplus area = 0.5*(80-30)*10=250.
c) What is the equilibrium quantity, consumer surplus, producer surplus and tax collections if the tax is imposed?
With a tax, consumers pay 20 more per unit than the price being charged, so Qd=50-0.5(P+20)=40-0.5P. Set this to Qs, and get 40-0.5P=0.2P-6 or 46=0.7P Solve for P to find P=65.7, but of course the consumers pay this plus the tax, so they pay 85.7. From the supply curve, when P=65.7, Q=7.15. Tax collections are Q*20=143. Consumer surplus = .5*(100-85.7)*7.15=51.1225. Producer surplus=127.63.
