econ

Microeconomics Homework

Problem 1: C(Q) = 100 + 20Q + 15Q^2 + 10Q^3
a) Fixed Cost (doesn’t change depending on output produced) = 100
b) Variable Cost of producing Q = 10 units: 20*10 + 15*10^2 + 10*10^3 = 200 + 1,500 + 10,000 = 11,700
c) Total Cost of producing Q = 10 units: C(10) = 100 + 20*10 + 15*10^2 + 10*10^3 = 11,800 Alternatively, we have Total Costs of Producing Q=10 units = Fixed Costs + Variable Costs of producing Q = 10 units = 100 + 11,700 = 11,800
d) Average Fixed Cost = Total Fixed Costs / Output = 100/10 = 10
e) Average Variable Cost = Total Variable Costs of producing Q= 10 units / Output = 11,700/10 = 1,170
f) Average Total Cost = Total Costs of producing Q=10 units / Output = 11,800/10 = 1,180
g) The marginal cost function is the derivative of the Total Short Run Cost Function. Thus MC(Q) for this cost function = 20 + 30Q + 30Q^2. At Q = 10, Marginal Cost = 20 + 300 + 3000 = 3320

Problem 2:(From Spencer: I think this problem is complete but don’t have my book on me. I will check when I get home tonight and if it isn’t I’ll finish it…)

Q
FC
VC
TC
AFC
AVC
ATC
MC
0 $15,000 $15,000

$- 100 $15,000 $15,000 $30,000 $150 $150 $300 $150
200
$15,000 $25,000 $40,000 $75 $125 $200 $100
300
$15,000 $37,500 $52,500 $50 $125 $175 $125
400
$15,000 $75,000 $90,000 $37.50 $188 $225 $375
500
$15,000 $147,500 $162,500 $30 $295 $325 $725
600
$15,000 $225,000 $240,000 $25 $375 $400 $775

Problem 3:

a. C(Q1,Q2) = 90 – 0.5Q1Q2 +0.4Q1^2 + 0.3Q2^2 C(Q1,0) = 90 + 0.4Q1^2 C(0,Q2) = 90 + 0.3Q2^2 For Q1 = 10, Q2 = 10: C(Q1,Q2) = C(10,10) = 90 - 0.5*10*10 + 0.4*10^2 + 0.3*10^2 = 90 – 50 + 40 + 30 = 110 C(Q1,0) = C(10,0) = 90 - 0.5*10*0 + 0.4*10^2 + 0.3*0 = 90 + 40 = 130 C(0,Q2) = C(0,10) = 90 - 0.5*0*10 + 0.4*0 + 0.3*10^2 = 90 + 30 = 120 Since C(Q1,0) +