Download October 20, 2006 - Version A in Word

ECMA04H - VERSION A
Sketchy Solutions to First Term Test, written on October 20, 2006
These are the answers to VERSION A.
Q1: C
On the PPF, if X = 7, Y = 20 - 12.8 = 7.2, so the point (7,7.4) is
unattainable
Q2: E opportunity cost of X = -dY/dX = .4(1+X); at X = 3, cost = 1.6
Q3: B opportunity cost of Y = -dX/dY at X = 5, -dY/dX = 2.4, so -dX/dY =
5/12
Q4: E V = 2X + 20 - .2(1+X)2 to maximize, set dV/dX = 0
dV/dX = 2 - .4(1+X) = 0 so .4(1+X) = 2, 1+X = 5, X = 4
Q5: F I is false because the PPF has nothing to do with tastes; II is true because
bowing out means that the opportunity cost of X rises as X increases; III
is true because the PPF is the boundary between attainable and
unattainable, indicating that there are limited amounts of X and Y, hence
scarcity.
Q6: A The rise in income shifts demand to the right
Q7: H If wages rise in the tennis racquet industry, supply shifts to the left.
Meanwhile, if golf clubs fall in price, this reduces the demand for tennis
racquets, because golf clubs and tennis racquets are substitutes. D
shifts left. Quantity clearly falls, but we are not sure what happens to
price, because the effects on P* go in opposite directions.
Q8: G If tennis court rentals fall in price, this increases the demand for tennis
racquets, because tennis courts and tennis racquets are complements. D
shifts right. Meanwhile, the technological innovation shifts supply to
the right. Quantity clearly rises, but we are not sure what happens to
price, because the effects on P* go in opposite directions.
Q9: I
The newspaper story increases the demand for tennis racquets, so D
shifts to the right; the fall in the price of the substitute (golf clubs)
reduces the demand, so D shifts to the left. So we don’t know which
way the demand curve shifts overall: if left, P* and Q* fall; if right, P*
and Q* rise; but if the two effects cancel out, then demand doesn’t
shift at all and nothing changes.
Q10: D If wages fall in the tennis racquet industry, supply shifts to the right.
The technological innovation also shifts supply to the right. Therefore,
P* falls and Q* rises.
Q11: B
Q12-15: The kink in the demand curve makes the computation a bit harder.
Q12: E If P = 3, then X = 18; consumer surplus is between the demand curve
and the $3 price line, but does not form a simple triangle and so you
must divide the consumer surplus area to work it out.
Q13: H If the consumer pays nothing for each additional unit, the consumer will
set X=36. The total value of these units to the consumer is the area
Q14: D
Q15: G
Q16: I
Q17: E
Q18: E
Q19-20
Q19: A
Q20: E
Q21: A
Q22: I
Q23-25:
Q23: H
Q24: C
Q25: B
under the demand curve, which can be found to be $114. If the allinclusive payment is F, then consumer surplus will be 114-F, and the
consumer will choose this option if 114-F>33. In other words, F
cannot be greater than $81.
If P = 6, then X = 4, and tax revenue = unit tax times X = $3 x 4 = $12
The deadweight area is no longer a simple triangle, but it can be
computed by dividing up the area. The correct answer is $17.
The demand curve can be obtained by setting P = dU/dX = 36(X+1)-.5
P = 4 = 36(X+1)-.5 so (X+1).5 = 9 so X+1 = 81 so X = 80.
U(80) = 72(81).5 - 72 = 576 and U(0) = 0 and PX = $320
So CS = 576 - 320 = $256.
You can do this by formulas, or intuitively by looking at graphs. I and
III are true statements.
dP/dQ = -b, so elasticity of demand = -(dQ/dP)(P/Q) = (1/b)(100/120)
= 5/(6b).
b = 2/3, so elasticity = 5/(6b) = 5/4
elasticity = 1 = 5/(6b), so b = 5/6
This is a hard question. TR = PQ
So dTR/dP = Q + PdQ/dP = Q[1 + (P/Q)dQ/dP] = Q[1 - elasticity]
If elasticity = 2/5 and Q = 600, then dTR/dP = 600[3/5] = 360
If P changes by .25, then TR changes by 360 x .25 = 90
BS/SS = elasticity of supply/elasticity of demand = 1.2/.3 = 4; thus
BS/SS = .8/.2 or BS = 8/10 or BS = .8
PB = 100 - Q and PS = 20 + (1/3)Q and PB = PS + 12
Thus 100 - Q = 32 + (1/3)Q or (4/3)Q = 68 or Q = 51
Q = 51 so PB = 100 - 51 = $49
Q = 51 so PS = 20 + (1/3)(51) = $37
As we have shown, changes in the law do not affect the buyers’ share
and the sellers’ share.