Assignment: Welfare evaluation

1.(a) If the government imposes a tax on cupcakes, raising their price by 20%, what is the measure of the economic loss suffered by consumers who buy cupcakes? Operationally, how would you measure the amount of this loss? Might firms that make cupcakes suffer a loss, too? What is the measure of their loss? (b) Draw the appropriate diagram that depicts these losses qualitatively.

2 (a) What is the indirect function? What does it show? (b) A consumer has an indirect utility function u = 8y p₁^-0.6 p₂^-0.4. His income is y=$3000; the price of good 1 changes from p1 = $4 to p₁ = $2, while p₂ = $3. Is the consumer better off as a result of this price change, worse off, or equally well off as before? Explain the reason for your answer.

(c) The maximum amount that the consumer would have been willing to pay for this price reduction is given by the compensating variation measure. Write down the algebraic equation which defines the compensating variation in this case.

(d) Now solve that equation - calculate the numerical value of the WTP for the price reduction in this case.

(e) The minimum amount of compensation that the consumer would have wanted to forego the price decrease is given by the equivalent variation - this is the WTA value of the price reduction. Write down the algebraic equation which defines the WTA value in this case (you don't need to solve the equation).

(f) If you solved the equation in (e) - you are not asked to solve it - do you expect that the WTA value would turn out to be the same as the WTP value in part (d), larger, or smaller? Explain your reason.

[Lecture: Demand and Welfare When Attributes Matter]

3. In this community in Yugoslavia there are two commodities; x1 is consumed especially by families with children and also, to a lesser extent, by families without children. x2 appeals the same to families with and without children. All families have the same utility function, which is given by

U(x₁,x₂) = 0.3ln(x₁ - C^0.75) + 0.7 ln x₂

where C is the number of children in the family. This is an example of what is known as a Stone- Geary utility function.

(a) Explain how having more children (i.e., a higher value of C) changes a family's preferences for x₁. Does this effect scale linearly with the number of children?

The corresponding indirect utility function is given by u = (y - p₁ C^0.75) / (p₁^0.30 p₂^0.7)

(b) Suppose there are two types of families in this community: families with no children and families with 4 children. This is an egalitarian country and all families have the same income, $25,000. Prices are p₁ = $4 and p₂ = $10. The national government introduces a type of child support payment program. It wants to give an income supplement to families with children so as to make them as well as off as other families with the same income but no children. How much should it give per child? [HINT: Use the indirect utility function to set up something like the equation for WTA]

4. A study of people's choice of transportation mode for commuting to work develops the following empirical estimate of the indirect utility function for using a given mode of transportation: u = 20 - 4 T - 12C, where u is the utility associated with travelling by that mode, T is the total time required for the trip, in minutes, and C is the total cost of the trip in dollars.

(a) Suppose that a particular consumer who has this indirect utility function faces a choice between two alternative travel modes: taking the bus to work takes 60 minutes and costs $1; driving to work takes 40 minutes but (with gas and tolls) costs $10. Which mode will that person choose? Explain the reasoning underlying your answer.

(b) What is the value of travel time for this consumer (the rate at which he would be willing to trade-off an extra minute of travel time for a reduced travel cost)?

(c) Suppose this indirect utility function represents the preferences of all commuters in the area. The city is considering a proposal to install a new light-rail transit system, similar in appearance to the existing bus transportation but with more capacity. It estimates that, overall, the new light- right would save 3 billion minutes of commuting time per year. The cost to construct the system, when put on an annual basis, would amount to $1.2 billion. Should the city go ahead and build the light-rail system? Explain your reason..

For the next question, lecture 2-22 Travel Cost.

5. The table below gives information on the distance from various nearby towns to the famous Cupcake Town Lake (distance is in miles). There is no admission fee. The only cost of visiting Cupcake Lake is the travel cost, which costs $1/mile. The researcher estimates the relationship between the number of visits per capita (per person), x, and the one-way travel cost from the town in which people live, p. He finds this demand function to be: x = 5 - 0.2*p .

(a) What is the cutoff price (the price at which demand falls to zero) with this demand function?

(b) Add columns to the table above identifying the cost of a visit to Cupcake Lake from each town, the predicted number of visits per capita from that town, and the total number of visits from the town (i.e., the visits per capita multiplied by the population).

(c) Why doesn't the researcher observe anyone coming from Delight to Cupcake Lake?

(d) Because of management costs, park managers are considering charging for admission to Cupcake Lake. They are considering an admission charge of $10/visit. Figure out (i) the new cost of visiting Cupcake from each town, (ii) the new number of visits per capita from each town, and (iii) the new total number of visits from each town (remember that negative visits count as zero).

(e) Suppose the authorities make improvements at Cupcake Lake (they build a boathouse), which only residents of Alabaster are allowed to use. In consequence, Alabaster resident's demand function for Cupcake lake changes to x = 8 - 0.2p. The demand functions of residents of the other towns do not change. What is the value of this improvement to Alabaster residents?

(f) Assume there is a $5 admission charge at Cupcake Lake. The County authorities are planning to open a new park at South Bend. South Bend is located 12 miles from Alabaster, 18 miles from Beautiful, 12 miles from Cornucopia, and 40 miles from Delight. For now, there will be no admission charge at South Bend Park. Which people will benefit from the opening of South Bend? How many visits will it attract annually? What is the aggregate gain in consumer's surplus associated with the opening of South Bend Park?

[Lecture on Firm Profit Maximization]

6. All-Leather is a tanning company in Chicago. Its total cost function is

C(QA) = 25 + 10QA + 4Q_A², where Q_A is leather production per week in thousands of pounds.

a) What is the formula for All-Leather's marginal cost function?

b) If leather sells for $1190 per thousand pounds, how much leather will All-Leather produce?

c) How much profit will All-Leather make?

[Based on BH pp 201-215; see also Lecture:Industry equilibrium and supply]

7. Slovak-Steel is the only steel factory in Slovakia. It burns coal in to produce steel. But, it is now required to abate the emissions from its use of coal.

(a) Suppose this emissions reduction raises (i) only Slovak-Steel's fixed costs of production, or (ii) only Slovak-Steel's variable costs of production, or (iii) both Slovak-Steel's fixed and variable costs of production. In each case, using both words and the appropriate diagrams, explain how emission reduction affects Slovak's supply curve of steel.

(b) The Slovakian steel industry grows over time as the economy expands, the demand for steel increases, and new firms have entered the steel industry in Slovakia. Pollution control regulations also change over time, and become more stringent. In its planning for a new round of tighter air pollution control regulations on its steel industry, the Slovakian government is considering grandfathering Slovak-Steel. How would grandfathering affect (i) Slovak-Steel, and (ii) firms that are thinking of entering the steel industry? How would grandfathering affect consumers of steel?

Lecture Market allocation and welfare.

8. (a) Suppose two different individuals finds themselves on a deserted island in the Pacific. Without knowing anything about the island, one person occupies the west end of the island, and the other occupies the east end. It subsequently turns out that there are certain stocks of fruits and vegetables lying around each end of the island. Is this a Pareto efficient allocation of those resources among the two individuals? Explain your reasoning. (b) Suppose that, having become aware of the fruits and vegetables on the island, the two individuals get together and exchange certain amounts of the fruits and vegetables among themselves; is that a Pareto efficient allocation of those resources? Explain your reasoning.