Units of X
10
5
0
5
10
Units of Y
15
15
MRS = -PX/PY = -15/5 = -3
The price must be greater than minimum AVC, which we have where AVC(Q) = MC(Q) or
3,000 -40Q +(1/2)Q2 = 3,000 – 80Q + (3/2)Q2
Q2 – 40Q = 0
Q = 40
Minimum AVC = 3,000 – 40(40) + (1/2)(40)2 = 2,200
Acme maximizes profit where MC(Q) = MR = P, or
3,000 -80Q + (3/2)Q2 = 12,350
(3/2)Q2 – 80Q – 9,350 = 0
Q= -(-80)±-802-4(32)-9,3502(32)=80±62,5003=80±2503=-56,67;110
Acme is earning an economic profit:
Profit = 12,350(110) – (600,000 + 3,000(110) – 40(110)2 + (1/2)(110)3)
= 1,358,500 – 1,111,500
= 247,000
We would expect firms to enter this industry, increasing the supply and lowering market price.
3600
2800
9
18
20
AVC
ATC
MC
$
Q
TFC = AFC
Q = (20 – 9)2,800 = 30,800 = 140K
K = 30,800/140 = 220
TVC = TC - TFC = 18(3,600) – 30,800 = 34,000 = 85L
L = 34,000/85 = 400
MC = w/MPL
MPL = w/MC = 85/18 = 4.72
|MRTS| = MPL/MPK = 4.72/6.25 = 0.76
>
0.61 = 85/140 = w/r
Q
20
15
10
5
0
5
10
20
15
P
S
D
EQ,P = (|
Q/NP)(P/Q) = (-1)(12/8) = -1.50
CS = ½ (10)(10) = 50
0 PS = 8(2) – ½ (2)(1) = +15
CSNew = ½ (8)(8) = 32
CS = 32 – 50 = -18
0 CS +
PS = - 18 + 15 = -3
leisure.
His MRS = - ½ (288/16) = - $9 per hour of leisure.
The overtime offer pays him, at the margin, $36/hour to reduce his leisure time.
He would b
0 units of capital and 20 units of labor to minimize costs.
Per Unit Cost = (wL + rK)/Q = [100(20) + 50(40)]/1000 = 4.00
PV= 1+0.060.08-0.0610= 530
∆Revenue= 100,0001+-1.12+120,000-0.05+0.04=-720
d first draw the MLC curve.
It has the same intercept as the ALC or Supply curve, but it has twice the slope.
Wage
200
Supply
150
100
50
Demand
200
150
100
50
Labor
= P
MPL
MPL = VMP/P = 110/2.75 = 40
= Revenue net of labor costs – Fixed Costs
= ½ (180)(90) – 7,800 = 8,100 – 7,800 = 300
Revenue net of labor costs – Fixed Costs
= ½ (120)(120) – 7,800 = 7,200 – 7,800 = - 600
Price=10,0001+0.00222=9,989.01
91201+ie10=1+0.040730
.0407301.039120-1=0.0439 or 4.39 percent
Q.
Thus its marginal revenue function is MR = 100 – (2/5)Q.
XYZ maximizes revenue if
XYZ maximizes profits if
0.243 + 0.231 + 0.179 + 0.151 = 0.804
0.2312 + 0.2432 + 0.0842 + 0.1792 + 0.1512) = 1869
= 10,000
2
0.179
0.151 = 541
1.43/0.78 < 2
– 2(0.20) < β4 < 0.88 + 2(0.20)
– 104.4(100) + 1.43(50,000) +0.88(100,000) = 46,104
=-104.4×10046,104=-0.23
Q1 = 30 and Q2 = 45.
Total output Q = 30 + 45 = 75.
The price we will charge:
(30)2 = 7600
(45)2 = 9725
A partial representation of Ellen’s tastes and preferences over
baskets of two goods, Good X and Good Y, is shown in the graph below:
Current market prices for Good X and Good Y are P
X
= 15 and P
Y
= 5.
Ellen’s income that she has
available to purchase X and Y is is M = 75.
She is a utility maximizer, and consumes integral quantities of
X and Y.
1.
Ellen’s
marginal rate of substitution
at her utility maximizing basket of X and Y equals ______ units
of Y per unit of X.
a)
-1/3
b) -2/3
c) -3/2
d) -2
e) -3
2.
The price of good X falls to P
X
= 5.
The price of good Y and Ellen’s income remain unchanged.
The change in Ellen’s quantity demanded of good X following this fall in the price of X due to the
substitution effect
equals _____ units of X.