Question

1. Let the production function beq Kili (K: capital, L: labor), the unit prices of capital and labor be both $1. (a) Find the cost function. 2b (b) If the firm with this production function is in a competitive market an many units of products should the firm produce? d the market price is S12, how 2. (a) Let the cost function be C(g)-F+mq G Is there economies of scale? (ii) If market price is equal to marginal cost, can the firm make profit? (b) Let the cost function be C(qi, q)-F+itqa (i) Is there economies of scope? (ii) If market prices are equal to marginal costs, can the firm make profit? 1+- 3. Consider a market with 2 identical firms. Each firm has cost function c(q)-q. The market demand is p-100-q. (i) Find the market equilibrium, price elasticity of demand at the equilibrium, and each firm's profit if the two firms choose output simultaneously and non-cooperatively. T, T, 91,322 60 7-u (i) Find the arkot quilbrium and.gch fim's polit if the two firms choose output to maximize their joint profit. I(こ言に「-25. T'=aL (iii) What is the percentage change in the profit of each firm. from (i) to (i)? 4.0% 4. (a) There is only one firm in a market. This firm has 100 plants, each produces according to cost
third question

the answer on the paper

process

Answer 1

Answer:

Question 3

i)

Given

For firm 1

Cost function C=q1^2

Market demand p=100-q=100-(q1+q2)

Total revenue for each firm TR=p*q1=(100-(q1+q2))*q1=100q1-q1^2-q1*q2

since each firm will try to maximize its profit so

MC=MR

MC=dC/dq1=2*q1

MR=dTR/dq1=100-2*q1-q2

So 2*q1=100-2*q1-q2

4*q1+q2=100 Eq 1

For firm 2

Cost function C=q2^2

Market demand p=100-q=100-(q1+q2)

Total revenue for each firm TR=p*q2=(100-(q1+q2))*q2=100q2-q2^2-q1*q2

since each firm will try to maximize its profit so

MC=MR

MC=dC/dq2=2*q2

MR=dTR/dq2=100-2*q2-q1

So 2*q2=100-2*q2-q1

4*q2+q1=100 Eq 2

From equation 1 and 2 we find equilibrium price and output

q1=20 units

q2=20 units

p=100-(20+20)=$60

Profit for firm 1

C=q1^2=20^2=$400

TR1=p*q1=60*20=$1200

Profit = TR1-C=1200-400=$800

Profit for firm 2

C=q2^2=20^2=$400

TR2=p*q2=60*20=$1200

Profit = TR2-C=1200-400=$800

ii)

If two firm collude then

Total cost for two firms TC= q1^2+q2^2

Total revenue for two firms TR=100q1-q1^2-q1*q2+100q2-q2^2-q1*q2

For profit maximization

MC1=MR1

MC1=dTC/dq1=2q1

MR1=dTR/dq1=100-2*q1-q2-q2

2q1=100-2*(q1+q2)

4*q1+2*q2=100 eq 3

MC2=MR2

MC2=dTC/dq2=2q2

MR2=dTR/dq2=100-2*q2-q1-q1

2q2=100-2*(q1+q2)

2*q1+4*q2=100 eq 4

From equation 3 and 4 we equilibrium output

q1=50/3 unit

q2=50/3 units

TC=q1^2+q2^2=(50/3)^2 + (50/3)^2 =$555.55

TR=100q1-q1^2-q1*q2+100q2-q2^2-q1*q2=100*(50/3)-(50/3)^2-(50/3)*(50/3)+100*(50/3)-(50/3)^2-(50/3)*(50/3)=$2222.22

p=100-(50/3 + 50/3)=$200/3

Profit for firm 1

C=q1^2=(50/3)^2=$2500/9

TR1=p*q1=(200/3)*(50/3)=$10000/9

Profit = TR1-C=10000/9- 2500/9=$833.33

Profit for firm 2

C=q2^2=(50/3)^2=$2500/9

TR2=p*q2=(200/3)*(50/3)=$10000/9

Profit = TR2-C=10000/9- 2500/9=$833.33

iii)

Percentage change in profit for firm 1= (833.33-800)*100/800=4.166%

Percentage change in profit for firm 2= (833.33-800)*100/800=4.166%