Question 1. The state of Delaland has two types of town. Type A towns are well-to-do, and type B towns are muchpoorer. Being wealthier, type A towns have more resources to spend on education; their demand curve foreducation is Q= 100−2P, where P is the price of a unit of education. Type B towns have demand curvesfor education which are given by Q= 100−4P.

  1. The cost of a unit of education is $20 per unit. How many units of education will the two types oftown demand?

Town A = Q= 100−2P

100 - (2*20)
## [1] 60

Town B = Q= 100−4P

100 - (4*20)
## [1] 20
  1. In light of the large discrepancies in educational quality across their two types of town, Delaland decides to redistribute from type A towns to type B towns. In particular, they tax type A towns by $5 foreach unit of education they provide, and they give type B towns $5 for each unit of education theyprovide. What are the new tax prices of education in the two towns? How many units of education do the towns now purchase?

Town A Price & Quantity

(20+5)
## [1] 25
100 - (2*25)
## [1] 50

Town B Price & Quantity

(20-5)
## [1] 15
100-(4*15)
## [1] 40
  1. Delaland wants to completely equalize the units of education across towns by taxing type A towns for each unit of education they provide and subsidizing type B towns for each unit of education they provide. It wants to do this in such a way that the taxes on type A towns are just enough to finance the subsidies on type B towns. If there are three type A towns for every four type B towns, how big a tax should Delaland levy on type A towns? How big a subsidy should they provide to type B towns?

4QS=3QT

S=0.75T

100 − 2(20 + T) = 100 − 4(20 − 0.75T)

100 - 40 -2T = 100 - 80 + 3T

60-2T=20+3T

40=5T

Taxes Quatity

40/5
## [1] 8

And Subsidies Quantity

0.75*8
## [1] 6

Question 2. Suppose you want to evaluate the effectiveness of vouchers in improving educational attainment by offeringa voucher to any student in a particular town who asks for one. What is wrong with simply comparing the educational performance of the students receiving vouchers with those who do not receive vouchers? What would be a better way to study the effectiveness of vouchers?

In such a study one may need to control for other variables that may have an impact on the students’ performance. Namely, poorer students may be more likely to request the voucher, these are also students who may have already been receiving very poor education. At the same time, students who request the voucher may be more inclined and motivated to learn as opposed to other students. These variables are usually closely correlated with academc performance, and may not necessarily be due to receiving (or not receiving) the voucher.

A better approach would be to control for these and other variables. This may include the random selection of studnets from various income levels and varying motivation levels, who have received the voucher and comparing them to another random group of students who not have received the voucher.

Question 3. Your utility function is U=√C, where C is the amount of consumption that you have in any given period. Your income is $40,000 per year, and there is a 2% chance that you will be involved in a catastrophic accident that will cost you $30,000 next year.

  1. What is your expected utility?

𝐸𝑈=1−𝑝×𝑈consumptionwithnoadverseevent+𝑝×𝑈consumptionwithadverseevent

When icome is 40000 and 10000

safe <- sqrt(40000)
unsafe <- sqrt(10000)
(1-0.02)*safe+(0.02*unsafe)
## [1] 198

Expected Utility is therfore 198

  1. Calculate an actuarially fair insurance premium.

Acturially fair premium

0.02*30000
## [1] 600

What would your expected utility be were you to purchase the actuarially fair insurance premium?

sqrt(40000-600)
## [1] 198.4943

note: 198.4943>198

  1. What is the most that you would be willing to pay for insurance, given your utility function?

198=sqrt(Wealth)

(198)^2
## [1] 39204
40000-39204
## [1] 796

$796