# econ

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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) +

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