Download 5-1.2 Consumer surplus is the monetary difference between what a

5-1.2 Consumer surplus is the monetary difference between what a consumer is willing to pay
for the quantity of the good purchased and what the good actually costs. When the
demand curve is linear, this is the area of the triangle under the demand curve and above
the price level. The demand curve intersects the vertical, price axis at a, the price is 0.5a,
so the height of the triangle is 0.5a. At a price of 0.5a, consumers demand
p = a – bq
0.5a = a – bq
q=
0.5a
units,
b
which is the length of the triangle. Thus, consumer surplus is
CS = 0.5a  0.5a 
CS =
0.5a
b
0.125a 2
.
b
According to the textbook footnote, consumer surplus lost (ΔCS) when price increase by
5 percent is
ΔCS = Rx(1 + 0.5εx),
where R is initial revenue, before the price increase, or p1 multiplied by Q1, x is the
percentage change in price, or Δp/p = (p2 – p1)/p1, and ε is the price elasticity of demand.
Rx is equal to A + 2B in the graph below (or A + B + C) and 0.5Rε(x2) is equal to triangle
B.
Assume the area of Rx can be expressed as A + 2B in the figure. Then, in the textbook
footnote equation, subtract triangle B from Rx to get the lost consumer surplus (A + 2B –
B = A + B). Triangle B is subtracted from Rx in the formula because the price elasticity
of demand is negative. (The price elasticity of demand and revenue are not provided in
this question, but in question 31 the price elasticity of demand is reported to be –0.6.)
6-4.6
a.
See figure.
b. See figure. Assume the number of copy machines K is fixed at 1. Then production
function is Q  1000 * min(L, 3). For L   3, Q  1000L; for L  3, Q  3000.
6-5.3
a.
This production always displays constant return to scale.
b. The Cobb-Douglas production function has decreasing, constant, or increasing
returns to scale as    is less than, equal to, or greater than 1.
c.
This production function has decreasing, constant, or increasing returns to scale as 
  is less than, equal to, or greater than 1.
d. The CES production function has decreasing, constant, or increasing returns to scale
as d is less than, equal to, or greater than 1.
7-2.3
a.Variable cost is
VC(q) = 10q – bq2 + q3.
Average variable cost is
AVC(q) = 10 – bq + q2.
For this to be positive,
10 – bq + q2 > 0
10 + q2 > bq
b < 10/q + q,
b. The average cost curve is U-shaped. AC is minimized at dAC/dq  Fq2  b  2q 
0.
c.
MC crosses AC when the functions are equal. MC  AC where 10  2bq  3q2  F/q 
10  bq  q2. MC  AVC where 10  2bq  3q2  10  bq  q2.
d. AVC is minimized where dAVC/dq  0.
dAVC/dq  – b  2q  0
or b  2q
MC  AVC
where
10  2bq  3q2  10  bq  q2.
Substituting 2q for b on both sides yields
10  q2  10 q2