Here are notes on the solution. This is not a complete answer to the exercise but it will let you check your work.
- The overall market without a hurricane looks like the diagram below. The price is $5, total consumption is 95, firm A supplies 18, and firm B supplies 77.
- After the hurricane hits and firm B is knocked off line, the market equilibrium would look like the graph below. The price would rise to $12, total consumption would fall to 60, and firm A's output would rise to 60.
- A price ceiling imposed at the original $5 price would cause the quantity to drop back to firm A's original quantity: 18. Relative to the post-hurricane equilibrium in 2, the change in PS would be a loss of areas A and B in the diagram below. The change in CS would be a gain of A and a loss of C.
The value of X is the WTP when Q is 18, which is $20.40. Computing the areas:
A = $7*18 = $126
B = 0.5*$7*(60-18) = $147
C = 0.5*($20.40-$12)*(60-18) = $176.40
Calculating the changes in PS, CS and SS:
`\Delta PS` = -($126 + $147) = -$273
`\Delta CS` = $126 - $176.40 = -$50.40
`\Delta SS` = -$273 - $50.40 = -$323.40
As expected, the price control reduces social surplus.
- Interestingly, this particular policy makes both suppliers and consumers worse off overall: consumers, who are the intended beneficiaries of the policy, see their CS fall under the control.
With that said, consumers who are able to buy gasoline are better off under the price control. However, MUCH less gasoline is available (60 down to 18, a drop of 70%), so many consumers will be hurt by being unable to buy gas. On balance, the harm suffered by people unable to buy gas exceeds the benefits to those who can.
- `MRS = (200-170)/(20-22) = -15 "hp"/"mpg"`
- Yes, although his preferences are unusual (he dislikes horsepower and fuel efficiency), they are complete (ranks all cars) and transitive (C>A>D>B>E>F).
- The graphs are shown below. For some of the people, too little information is given to determine the slopes of their indifference curves precisely.
Person 1 regards hp and mpg as perfect substitutes at a 15:1 ratio; Person 2 cares only (or mostly) about mpg; and person 3 cares only (or mostly) about hp. Person 4's preferences are odd: he basically likes poor quality cars: low hp and low mpg. Because 4's preferences are complete and transitive, however, they are rational.
- The graph is shown below. All bundles in set A are feasible. The slope of the budget constraint, `m`, is:
`m = -P_n/P_m = -16/8 = -2`
- Assuming the tickets cannot be sold, the new budget constraint looks as shown below. The free tickets have added the bundles in area B to the original feasible set.
- The new budget constraint is shown below and the new feasible set is shaded. Note that the x-intercept is not affected. For reference, the original BC is also shown.
- Adding the time constraint to the original diagram produces the graph below. The slope of the time constraint is -10/3 = -3.33, which is steeper than the money BC. The student's feasible set is the shaded area, which extends from the origin up to 9 movies, down along the money BC to the point where the two BCs cross, down along the time constraint to 3 novels, and then back to the origin.
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Peter J Wilcoxen, The Maxwell School, Syracuse University