ECN 100
Name____ANSWERS___
SSI 10
Midterm
(16 pts) 1.
Consumer Surplus
(20 pts)1. (a) Consider the following linear supply and demand relationships:
Demand: P = 100 – Q
Supply: P = 40 + Q
Obtain consumers’ surplus and producers’ surplus (both graphically and algebraically).
S = D  p = 70 and Q =30
Consumer Surplus: CS= area (A+B+C)
= ½ (30)(30) =450
Producer Surplus: PS= area (D+E+F)
= 30*30*1/2=450
S’
P
A
70
B
S
C
D
E
F
30
(b) The government imposes a sales tax of $6 per unit. Then we have:
Demand: P = 100 – Q
Supply: P = 40+ 6 + Q
Obtain the new consumers’ surplus and producers’ surplus. Show your answers in the
graph for part (a).
S = D  Q = 16 and P = 42
New CS = area A = ½ (50 – 42)(16) = 64
New PS = area F = ½ (36 – 20)(16) = 128
(c) Compute government revenue and deal weight loss (DWL). Show your answers in the
graph for part (a).
Gov. Rev. = area (B+D) = 6*16 = 96
DWL = area C + area E = ½ (42 – 40)(20 -16)+ ½ (42 – 36)(20 -16) = 4 + 8=12
Q
(12 pts) 2.
Suppose that the long-run world demand and supply elasticities of crude oil
are -0.906 and 0.515, respectively. The current long-run equilibrium price is $30
per barrel and the equilibrium quantity is 16.88 billion barrels per year. Derive the
linear long-run demand and supply equations.
Answer: If the demand curve is linear, it is in the form of QD = a + bP. Also, we know
that
E = b (P/Q)
b = E (Q/P )= -0.906 (16.88/30) = -0.510.
Rearranging the linear expression for demand allows us to solve for a as follows:
a = QD - bP
a = 16.88 + 0.510(30) = 32.180.
We may now write the linear expression for demand as
QD = 32.18 - 0.510P.
If the supply curve is linear, it is in the form of
QS = c + dP. Also, we know that E = d (P/Q)
d = E (Q/P) = 0.515 (16.88/30)= 0.290.
Rearranging the linear expression for demand allows us to solve for c as follows:
c = QS - dP
c = 16.88 - 0.290(30) = 8.18.
We may now write the linear expression for supply as
QS = 8.18 + 0.290P.
(6 pts) 3.
In Japan, restrictions on the import of rice keep the price of rice at above 10 times the
world level. Suppose that these restrictions were relaxed. (a) Show how this change
would affect the equilibrium bundle of a Japanese consumer. (b) Decompose the change
into income and substitution effects.
(8 pts) 4.
Conditional Cash Transfer (CCT) programs aim to reduce poverty by making
welfare programs conditional upon the receivers' actions. The government only transfers
the money to persons who meet certain criteria. These criteria may include enrolling
children into public schools, getting regular check-ups at the doctor's office, receiving
vaccinations, or the like.
a) Using a diagram show the likely effect of the program on the consumption of
schooling/Health care and all the other goods (AOG) for the targeted individuals.
b) Using a diagram show possible differences between the effects of a CCT program and
that of unconditional cash transfer on welfare. Take a position is supporting one of the
programs (or against both of them if you like neither) and motivate it.
(18 pts) 5. Cyrus considers changing jobs and moving from L.A. to San Francisco. He currently
earns $4000/month and pays $0.8/sq ft rent a month. In SF, he has to pay $1.2/sq ft rent a
month. For him, the non-economic pros and cons of the move balance out, so that he is
willing to make his decision on economic grounds. His utility derived from housing x and
all other goods is given by u(x,y) = x.y
a. Depict Cyrus’s current choice between housing and other goods in a graph.
b. Would Cyrus take the job in SF if it pays $4800?
c. Calculate the minimum income (M’) that his prospective employer in SF has to offer
Cyrus to make him consider moving to SF. What does this extra income (M’-M)
measure and what is it called?
(28 pts) 6.
Mike has preferences over x (= Fun measured in hours per day) and y (= Other
Goods measured in $/day) are represented by the utility function: u=u(x,y)
(1) Set up the consumer problem.
(2) Show the solution to the consumer’s problem graphically (label your graph carefully)
(3) Characterize Mikes the optimal choice mathematically (Hint: state the two conditions that
must hold at the optimum)
(4) Derive Nader’s Marshallian demand curve graphically
(5) Show Income effect and Substitution effect of a price increase using a graph.
(6) Assume the following Cobb-Douglas utility function: u(x,y) = xy2
.
a. Solve for the Marshallian demand functions of x and y.
b. Use the Tangency Condition (MRS = p/q) and the Budget Equation (px + qy =
m) to get the demand functions:
x = [1/3](m/p),
y = [2/3](m/q)
b. Show that for m = 100, p = 1, and q = 1, Mike’s optimal choice is x = 33.33 and y = 66.67.
(18 pts) 7.
Hicksian Demand Function (each part 3 pts)
Nader has preferences over two goods x (measured in pounds/day) and y (=Other Goods
measured in terms of $/day) are presented by u = u(x, y). Nader faces market prices p and q (for
x and y respectively. Mike has m = $/day available to spend.
(1) Set up Mike’s expenditure Minimization problem and conceptually write the solution to this
problem (Hint: minimum expenditure function)
(2) Derive Nader’s Hicksian demand curve graphically
(3) Assume the following Cobb-Douglas utility function: u(x,y) = xy2. The minimum
expenditure function for this utility function is: E=U_bar (3p)(3q/2)2 or simply
E = 6.75U_bar pq2.
a. Find Hicksian or compensated demand curve for x.
b. If m = 100, p = 2, and q = 1, Mike’s optimal choice is x = 16.7 and y = 66.67.
i.
Show that that Mike’s utility level at x = 16.7 and y = 66.67 is 74074.
ii. How much is Mike worse off as a result of this price increase (calculate the CV).
iii. Find Mike’s Hicksian demand for x when p=2.