Specialized microeconomics Practice excercise - Kinh tế vĩ mô | Trường Đại học Kinh tế, Đại học Quốc gia Hà Nội

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Profile Phạm Thị Huyền
lOMoARcPSD|45316467
lOMoARcPSD|45316467
Specialized microeconomics
Practice excercise
Ex 1:
a) What is increasing/ constant/ diminishing return to scale ?
b) What is the diminishing of marginal utitlity law. Can you give an example to
illustrate ? Ex 2:
a) What is Giffen goods ? Can you give an illustrous example?
b) Explain about Engel curve
Ex 3:
Explain about the changes of budget constraint line depended on the the change of good’s
price and the change of consumer’s income ?
Ex 4:
When will intertemporal budget contraint line become steeper ? Explain why ?
Ex 5:
In a purely competitive market a firm’s marginal revenue is always equal to what? A
profit-maximizing firm in such a market will operate at what level of output?
Ex 6:
If average variable costs exceed the market price, without fixed cost, what level of output
should the firm produce?
Ex 7:
A student states that “Monopolist will choose to produce in a market with inelastic
demand curve”. This statement is True or False? Explain why ?
Ex 8:
Suppose your opponent is not playing his Nash equilibrium strategy. Should you play your
Nash equilibrium strategy?
Ex 9:
A typical consumer bought 24 music tracks, q1, per quarter and consumed 18 units of live music,
q2, per quarter. This average consumer’s Cobb-Douglas utility function as: U = q1
0.4
q2
0.6
. What
is marginal rate of substitution of this consumer if q1 = 24, q2 = 18?
lOMoARcPSD|45316467
Ex 10:
a) What is inverse demand function?
b) True or false? If the demand function is x1 = −p1, then the inverse demand function is x
= −1/p1.
Ex 11: A computer assembly firm’s production function is q = 0.1LK + 3L
2
K - 0.1L
3
K.
a) What is its short-run production function if capital is fixed at K = 10?
b) Determine the marginal product of labor (MPL) and average product of labor (APL) in
this case
Ex12: Eric purchases food (measured by x) and clothing (measured by y) and has the utility
function U (x, y) = xy. He has a monthly income of $800. The price of food is Px = $20, and
the price of clothing is Py = $40
Ex13: A monopolist faces demand function: Q(D) = 75-0.5p and variable cost VC=
0.5q
2
, FC=500. Find the price and quantity produced for firm’s profit maximization?
Ex14: The inverse market demand of a homogeneous product in Cournot duopoly is
P= 200 -3Q, with (Q = quantity produced of each firm = Q1+Q2). Total cost of each firm
TC1= 26Q1 and TC2 = 32Q2. Calculate each firm’s equilibrium output and the market price ?
Ex 15: The inverse market demand of a homogeneous product in Stackelberg duopoly is
P= 16000 -4Q, with (Q = quantity produced of each firm = Q1+Q2). Total cost of each firm
TC1= 4000Q1 and TC2 = 6000Q2. Suppose firm 1 reacts as quantity leader and firm 2 as quantity
follower. Calculate each firm’s equilibrium output and the market price ?
Ex 16: The monopolist faces a demand curve given by D(p) = 10p
−3
. Its cost function is
c(y)=2y. What is its optimal level of output and price?
Ex 17: In pure competition, a firm has a cost function given by c(y) = 10y
2
+ 1000.
lOMoARcPSD|45316467
a) What is its supply curve?
b) what output is average cost minimized
Ex 18: In oligopolistic market, there are 2 firms which compete each other. Demand curve of the
industry has type: P= 150-Q. Both firms has similar cost function: TC = 30Q + 500.
Suppose each firm reacts following Cournot equilibrium.
a) Find quantity and price in Cournot equilibrium ? What’s the profit of each firm ?
b) Suppose firm 1 changes its cost function into: TC1 = 18Q1 +500, while firm 2 fixes the cost
function: TC2 = 30Q2 + 500. How will quantity change in new equilibrium ? Find the market
price, and profit of each firm ?
Ex 19:
a) Consider the production function f (x1, x2) = x1
2
x2
3
Does this exhibit constant, increasing,
or decreasing returns to scale?
b) Consider the production function f (x1, x2) = 5x
1/2
x
1/3
Does this exhibit constant, increasing,
or decreasing returns to scale?
Ex 20: If two goods are perfect substitutes, what is the demand function for good 1?
lOMoARcPSD|45316467
Hint:
7) False. Monopolist will choose to produce in highly elastic demand market
8) No. but if your component does not follow Nash equilibrium strategy, it might have a
better strategy for you to pursue.
9) MRS= -MU1/ MU2 = - (0.4 q1
-0.6
q2
0.6
) / (0.6q1
0.4
q2
-0.4
) = - = - = -0.5
10) a) The inverse demand function measures the price at which a given quantity will
be demanded.
b) False
11)
a) q =L + 30L
2
- L
3
.
b) MPL=1+60L-3L
2
AP
L
=1 + 30L - L
2
.
12) MUx =y and MUy =x. Based on equations of budget constraint and preference
optimization. -> x = 20, y =10
13) Find MR, Put MR=MC for profit maximization -> q= 30, p=90
14) Find MR1 and MR2. Profit maximization -> MR1 =MC1 and MR2 =MC2 -> find reaction
curve of each firm: Q1= 29-0.5Q2 and Q2= 28-0.5Q1 -> solve set of equations -> q1= 20; q2=
18 and P= 86
15) Find the follower’s reaction function: Q2=1250-0.5Q1. Firm 1- leader can foresee firm
2’s quantity -> P= 16000-4Q1 -4Q2. = 16000-4Q1 -4 (1250-0.5Q1) = 11000-2Q1. -> TR1.
Profit maximization condition: MR1=MC1-> Q1 = 1750, Q2 =375, P=7500
16) p
3
= 10/y -> p = 10
1/3
y
-1/3
-> TR(y) = 10
1/3
y
2/3
-> MR= 2/3. 10
1/3
. y
-1/3
MC= 2
Profit maximization condition: MR= MC
2/3. 10
1/3
. y
-1/3
= 2 -> 10
1/3
. y
-1/3
= 3 -> y
1/3
= 10
1/3
/3 -> y= 10.
3
-3
p= 10
1/3
10
-1/3
. 3 = 3
17)
a) MC = 20y
In pure competition p = 20y, so the supply curve: y = p/20.
lOMoARcPSD|45316467
b) AC= 10y + 1000/y
To minimize the average cost, set AC equals
MC 10y + 1000/y = 20y. Solve to get y∗ = 10.
18) a) Marginal cost of each firm: MC =
30 Market demand: P = 150- Q1 – Q2
TR of firm 1: TR1 = 150Q1- Q
2
1 – Q1Q2
MR of firm 1: MR1 = 150 - 2 Q1 - Q2
Profit maximization: MR = MC
->150-2Q1-Q2=30
->Q1=60–½Q2
Similarly, reaction curve of firm 2:
Q2=60–½Q1
-> Q1= Q2 = 40
-> P = 150- 40-40 = 70
-> TR -TC = 1100
b) MC1 = 18; MC2 = 30
Profit maximization: MR=MC
->150-2Q1-Q2=18
-> Q1= 66- ½ Q2
Reaction curve of firm 2 has the same structure as a).
Q2=60–½Q1
-> Q1= 66- ½ (60 – ½ Q1)
->Q1=48,Q2=36
Quantity of each firm: Firm 1 increases while Firm 2 decreases
Market price: P= 150- 48-36= 66
Profit of firm 1:
Profit of firm 2: = 796
lOMoARcPSD|45316467
19) a) Increasing returns to scale. The output increases in a greater proportion than the increase
in input. b) Decreasing returns to scale. The output increases in a smaller proportion than the
increase in input (if we double inputs, the output increases 1.78).
20) The demand for good 1 is zero when p1 > p2, any amount on the budget line (between 0 and
m/p1) when p1 = p2, and m/p1 when p1 < p2.
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lOMoARcPSD|45316467 lOMoARcPSD|45316467 Specialized microeconomics Practice excercise Ex 1:
a) What is increasing/ constant/ diminishing return to scale ?
b) What is the diminishing of marginal utitlity law. Can you give an example to illustrate ? Ex 2:
a) What is Giffen goods ? Can you give an illustrous example? b) Explain about Engel curve Ex 3:
Explain about the changes of budget constraint line depended on the the change of good’s
price and the change of consumer’s income ? Ex 4:
When will intertemporal budget contraint line become steeper ? Explain why ? Ex 5:
In a purely competitive market a firm’s marginal revenue is always equal to what? A
profit-maximizing firm in such a market will operate at what level of output? Ex 6:
If average variable costs exceed the market price, without fixed cost, what level of output should the firm produce? Ex 7:
A student states that “Monopolist will choose to produce in a market with inelastic
demand curve”. This statement is True or False? Explain why ? Ex 8:
Suppose your opponent is not playing his Nash equilibrium strategy. Should you play your Nash equilibrium strategy? Ex 9:
A typical consumer bought 24 music tracks, q1, per quarter and consumed 18 units of live music,
q2, per quarter. This average consumer’s Cobb-Douglas utility function as: U = q1 0.4 q2 0.6. What
is marginal rate of substitution of this consumer if q1 = 24, q2 = 18? lOMoARcPSD|45316467 Ex 10:
a) What is inverse demand function?
b) True or false? If the demand function is x1 = −p1, then the inverse demand function is x = −1/p1.
Ex 11: A computer assembly firm’s production function is q = 0.1LK + 3L2K - 0.1L3K.
a) What is its short-run production function if capital is fixed at K = 10?
b) Determine the marginal product of labor (MPL) and average product of labor (APL) in this case
Ex12: Eric purchases food (measured by x) and clothing (measured by y) and has the utility
function U (x, y) = xy. He has a monthly income of $800. The price of food is Px = $20, and
the price of clothing is Py = $40
Ex13: A monopolist faces demand function: Q(D) = 75-0.5p and variable cost VC=
0.5q2, FC=500. Find the price and quantity produced for firm’s profit maximization?
Ex14: The inverse market demand of a homogeneous product in Cournot duopoly is
P= 200 -3Q, with (Q = quantity produced of each firm = Q1+Q2). Total cost of each firm
TC1= 26Q1 and TC2 = 32Q2. Calculate each firm’s equilibrium output and the market price ?
Ex 15: The inverse market demand of a homogeneous product in Stackelberg duopoly is
P= 16000 -4Q, with (Q = quantity produced of each firm = Q1+Q2). Total cost of each firm
TC1= 4000Q1 and TC2 = 6000Q2. Suppose firm 1 reacts as quantity leader and firm 2 as quantity
follower. Calculate each firm’s equilibrium output and the market price ?
Ex 16: The monopolist faces a demand curve given by D(p) = 10p−3. Its cost function is
c(y)=2y. What is its optimal level of output and price?
Ex 17: In pure competition, a firm has a cost function given by c(y) = 10y2 + 1000. lOMoARcPSD|45316467 a) What is its supply curve?
b) what output is average cost minimized
Ex 18: In oligopolistic market, there are 2 firms which compete each other. Demand curve of the
industry has type: P= 150-Q. Both firms has similar cost function: TC = 30Q + 500.
Suppose each firm reacts following Cournot equilibrium.
a) Find quantity and price in Cournot equilibrium ? What’s the profit of each firm ?
b) Suppose firm 1 changes its cost function into: TC1 = 18Q1 +500, while firm 2 fixes the cost
function: TC2 = 30Q2 + 500. How will quantity change in new equilibrium ? Find the market
price, and profit of each firm ? Ex 19:
a) Consider the production function f (x 2 3
1, x2) = x1 x2 Does this exhibit constant, increasing,
or decreasing returns to scale?
b) Consider the production function f (x1, x2) = 5x1/2 x1/3 Does this exhibit constant, increasing,
or decreasing returns to scale?
Ex 20: If two goods are perfect substitutes, what is the demand function for good 1? lOMoARcPSD|45316467 Hint:
7) False. Monopolist will choose to produce in highly elastic demand market
8) No. but if your component does not follow Nash equilibrium strategy, it might have a
better strategy for you to pursue. 9) MRS= -MU -0.6 0.6 0.4 -0.4 1/ MU2 = - (0.4 q1
q2 ) / (0.6q1 q2 ) = - = - = -0.5
10) a) The inverse demand function measures the price at which a given quantity will be demanded. b) False 11) a) q =L + 30L2 - L3. b) MPL=1+60L-3L2 APL =1 + 30L - L2.
12) MUx =y and MUy =x. Based on equations of budget constraint and preference
optimization. -> x = 20, y =10
13) Find MR, Put MR=MC for profit maximization -> q= 30, p=90
14) Find MR1 and MR2. Profit maximization -> MR1 =MC1 and MR2 =MC2 -> find reaction
curve of each firm: Q1= 29-0.5Q2 and Q2= 28-0.5Q1 -> solve set of equations -> q1= 20; q2= 18 and P= 86
15) Find the follower’s reaction function: Q2=1250-0.5Q1. Firm 1- leader can foresee firm
2’s quantity -> P= 16000-4Q1 -4Q2. = 16000-4Q1 -4 (1250-0.5Q1) = 11000-2Q1. -> TR1.
Profit maximization condition: MR1=MC1-> Q1 = 1750, Q2 =375, P=7500
16) p3 = 10/y -> p = 101/3 y -1/3 -> TR(y) = 101/3 y2/3 -> MR= 2/3. 101/3. y-1/3 MC= 2
Profit maximization condition: MR= MC
2/3. 101/3. y-1/3 = 2 -> 101/3. y-1/3 = 3 -> y1/3= 101/3 /3 -> y= 10. 3-3 p= 101/3 10 -1/3. 3 = 3 17) a) MC = 20y
In pure competition p = 20y, so the supply curve: y = p/20. lOMoARcPSD|45316467 b) AC= 10y + 1000/y
To minimize the average cost, set AC equals
MC 10y + 1000/y = 20y. Solve to get y∗ = 10.
18) a) Marginal cost of each firm: MC =
30 Market demand: P = 150- Q1 – Q2
TR of firm 1: TR1 = 150Q1- Q21 – Q1Q2
MR of firm 1: MR1 = 150 - 2 Q1 - Q2 Profit maximization: MR = MC ->150-2Q1-Q2=30 ->Q1=60–½Q2
Similarly, reaction curve of firm 2: Q2=60–½Q1 -> Q1= Q2 = 40 -> P = 150- 40-40 = 70 -> TR -TC = 1100 b) MC1 = 18; MC2 = 30 Profit maximization: MR=MC ->150-2Q1-Q2=18 -> Q1= 66- ½ Q2
Reaction curve of firm 2 has the same structure as a). Q2=60–½Q1
-> Q1= 66- ½ (60 – ½ Q1) ->Q1=48,Q2=36
Quantity of each firm: Firm 1 increases while Firm 2 decreases
Market price: P= 150- 48-36= 66 Profit of firm 1: Profit of firm 2: = 796 lOMoARcPSD|45316467
19) a) Increasing returns to scale. The output increases in a greater proportion than the increase
in input. b) Decreasing returns to scale. The output increases in a smaller proportion than the
increase in input (if we double inputs, the output increases 1.78).
20) The demand for good 1 is zero when p1 > p2, any amount on the budget line (between 0 and
m/p1) when p1 = p2, and m/p1 when p1 < p2.