econ

Topics: Costs, Marginal cost, Variable cost Pages: 8 (1235 words) Published: December 4, 2013
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) + C(0,Q2) = 250 > C(Q1,Q2) = 110, Economies of Scope does exist. b. Cost complementarities exist in a multi-product cost function when the marginal cost of producing one output is reduced when the output of another product is increased. Differentiating the cost function with respect to Q2:

MC2(Q1,Q2) = -0.5Q1 + 0.6Q2
With respect to Q1:
MC1(Q1, Q2)= -0.5Q2 + 0.8Q1

Clearly, cost complementarities exist. If we increase the quantity of product 1 being produced, the marginal cost of producing product 2 decreases. Additionally, the marginal cost of producing product 1 is a decreasing function of product 2. Thus, the two products are cost complementary.

c. The marginal cost of producing product 1 is given by the following:

MC1(Q1, Q2) = -0.5*Q2 + 0.8*Q1

If the firm sells the division, the marginal cost function becomes:

MC1(Q1, 0) = 0.8*Q1

Thus, due to the sale of the division, the marginal cost of producing product 1 goes up by .5 times the number of units of Q2 that were being produced prior to the sale.

d. Cost complementarity: a0

Looking at the two conditions, it is clear that if a Q = 10
P=9-10/4=$6.50
Profits= P*Q - C(Q) = 6.5*10 - (124-16*10 + 10^2) = 1
Additional firms will enter the market to capture economic profits. In the equilibrium condition under monopolistic competition, economic profits will be zero.

Problem 7:
The inverse market demand function is P = 200 - 3(Q1 + Q2)
This is of the form P = a - b(Q1 + Q2)
We see that a = 200; b = 3
The Cost function for firm 1 => C1(Q1) = 26Q1 => Marginal Cost = 26 The Cost function for firm 2 => C2(Q2) = 32Q2 => Marginal cost = 32

(a) Firm 1’s Marginal Revenue function = 200 - 3Q2 - 6Q1
Firm 2’s Marginal Revenue function = 200 - 3Q2 - 6Q2
Both firms will produce to maximise their profits. Hence, they will produce such that Marginal Revenue = Marginal Cost and this will give us the reaction functions Therefore, we get the reaction functions as follows:

Firm...
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