Fall 2012 Exam 2 Solution

Here are the final numerical results for each section of the exam.  You can use them to check your work if you do the exam for practice.  If you have trouble with the problems, or don't get the answers shown here, stop by during office hours or make and appointment and we can go over them.

Question 1

(a) Household B has Cobb-Douglas preferences; a = 0.4.

(b) X = 32; Y = 60.

(c) Graph.

Question 2

(a) Derivation omitted; result is M = U * (Px/a)^a * (Py/(1-a))^(1-a)

(b) Expenditure = $984.

(c) CV = $984 - $1,200 ($900+$300) = -$215.  Better off by $215.

Question 3

(a) Derivation omitted; results are X = b*M/(b*Px+Py), Y = M/(b*Px+Py).

(b) Household C has PC preferences with b = 3.

(c) X = 87, Y = 29, Expenditure for original U = $1,596. CV = $1,596 - $1,653 ($1,344+$309) = -$57.  Household is better off.

Question 4

(a) X = 175, Y = 25.

(b) X = 132, Y = 0.

(c) Expenditure needed for original U: $4,700.  CV = $4,700-$3,300 = $1,400.  Household is worse off.

(d) Revenue = $1,188.  Not required: DWL = $1,400 - $1,118 = $212.

Question 5

(a) Graph.

(b) Compensated equilibrium: X = 160, Y = 43.75.  Substitution effect (changes in X): 160-175 = -15.  Income effect: 132-160 = -28.  Total effect: 132-175 = -43.

Question 6

(a) Household H, new equilibrium: X = 196, Y = 100.

(b) Share spent on X.  L: 132*$25/$3,300 = 100%. H: 196*$25/$6,500 = 75%.

(c) Tax revenue.  L: 132*$9 = $1,188. H: 196*$9 = $1,764.

(d) Effective tax rates (tax payments as a share of income):  L = $1,188/$3,300 = 36%. H = $1,764/$6,500 = 27%.  Since the effective tax rate is higher on low income households the tax is regressive.

(e) Good X is a necessity and has an income elasticity less than one: as income goes up, consumption of X does not increase in proportion.  For a 97% increase in income ($3,200/$3,300), consumption of X increases 48% (64/132), so the income elasticity is about 0.5.