A firm has two production plants where they produce the same product. The cost f

ID: 1181087 • Letter: A

Question

A firm has two production plants where they produce the same product. The cost function at plant #1 is (C_{1}(Q_{1})=10Q_{1}+.5Q_{1}) The cost function at plant #2 is (C_{2}(Q_{2})=10Q_{2}+2Q_{2}^{2})

A) If the firm wants to produce Q total units of output, what fraction of Q will be produced at plant #1? What fraction at plant #2? Show all work. B) What is the firms total cost function in terms of Q? Show all work. A) If the firm wants to produce Q total units of output, what fraction of Q will be produced at plant #1? What fraction at plant #2? Show all work. B) What is the firms total cost function in terms of Q? Show all work.

Explanation / Answer

marginal cost of plant 1

MC(Q1)=d/dQ {C1(Q1)} = d/dQ (10Q1 + 0.5Q1)

MC(Q1)= d/dQ (10Q1 + 0.5Q1)

MC(Q1) = 10+0.5 = 10.5

marginal cost of plant 2

MC(Q2)=d/dQ {C2(Q2)} = d/dQ (10Q2 + 2(Q2)^2)

MC(Q2)= 10 + 4Q2

(a)

The plant 1 has a lower marginal cost with respect to plant 2, so it should distribute its production in such a way that MC1(Q1) = MC2(Q2) Because MC2 > MC1, this means that Q1 should be greater than Q2 in order for this equation to balance out.

here Q1+Q2 =Q

so ratio of quantitly produce by plant 1 and plant 2 are...

Q2/Q1 = MC1/MC2

Q2/Q1 = 10.5/(10 + 4Q2).......(1)

by solving eq 1

10Q2 +4(Q2)^2 = 10.5Q1

Q1 = [10Q2 +4(Q2)^2]/(10.5)

Q1 = 0.95Q2+0.38(Q2)^2

Q= Q1+Q2

put the value of Q1

Q= 0.95Q2+0.38(Q2)^2+Q2

Q= 1.95Q2+0.38(Q2)^2

using quarditic equation formula

Q2 = {-1.95+sqrt[(3.8)-1.52Q]}/0.76

Q2 = {-1.95-sqrt[(3.8)-1.52Q]}/0.76

and Q1= Q-Q2

so the fraction of Q will be produced at plant #2

Q2 = {-1.95+sqrt[(3.8)-1.52Q]}/0.76

and

the fraction of Q will be produced at plant #1

(b)

for firms total cost function in terms of Q

put the value of Q1 or Q2 in terms of Q in cost equation we can find total cost equation.

thnq

Navigate

A firm has two plants, one in theUnited States and one in Mexico, and it cannot

A firm has unlevered beta of 1.1, and now its debt to equity ratio is 0.4. What

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.

A firm has two production plants where they produce the same product. The cost f

Question