Maths Part Flashcards
Your market research department has found out that the demand curve for chocolate is
Q(P) = 16 − 0.6P . The current price of chocolate is 20. What is the price elasticity of demand at this price (round to two decimals if necessary)?
Q’(P) * P/Q
El = -0.6 * (20)/(16-0.6*20)
In the perfectly competitive market for Easter eggs all producers have the same total cost function
C (q) = 108+3q2. Suppose that market demand is given by
Q(P ) = 4200−100P .
How many producers will operate in this market in the long run?
find MC, ATC => equal them:
6q = 108/q + 3q => q=6
MC=P
Find P by inverse demand fct =>
P= -Q/100 +42
36= -Q/100 +42
Q=600 ==> 600/6 = 100
A firm in a perfectly competitive market has the cost function
C (q) = 1/4 q2 + 10q.
The short-run market price is given by P = 25. How much should the firm produce in the short run?
MC = P
0.5q + 10 = 25
=> q = 30
Consider a perfectly competitive market. The demand curve is given by Q(P ) = 98 − 4P
The market supply curve is
Q(P ) = 10P
How high is the social surplus in equilibrium?
Demand:
98 - 4P => P = 24,5
Supply:
98 - 4P = 10P
98 = 14P => P = 7
Q=10P => Q= 70
24,5*70/2 = 857,5
Consider a perfectly competitive market. The demand curve is given by P (Q) = 30 − 1.5Q
and the supply curve is given by
P (Q) = 6 + 0 . 5Q.
The government introduces a tax: each consumer must pay €8 to the government for every unit the consumer buys. How high is the tax revenue?
30 - 1.5Q = 6 + 0.5Q
Q = 12
New supply curve:
P(Q)= 6 + 8 +0.5Q
==>
30 - 1,5Q = 14 + 0.5Q
Q = 8
Income government:
Q1tax => 88 = 64
Consider the perfectly competitive market for jeans in Italy. Domestic demand is Q(P ) = 1000 − 20P
and domestic supply is
Q(P ) = 20P − 200.
There is free trade. Initially, the
world market price is 35, then it drops to 20. Which of the following statements is correct?
1000 - 20P = 20P - 200
P = 30
———–
q = 20(30) - 200
q = 400
————
q = 20(35) - 200
q = 500
==> 500-400= 100 => 100*20 = 2000
A monopoly faces market demand Q(P) = 30−P
and has the cost function
C (Q) = 0.5Q2.
What is the monopolist’s profit?
Inverse demand fct: P = 30 - Q
,times by Q for revenue:
30Q - Q^2 and so MR=30-2Q
MC=Q
MR=MC => 30-2Q=Q => Q=10
we can now calculate profit:
rev-cost= (300-Q^2)-(0.5Q^2)
=> 3010-10^2 - 0.5100
=> 150
Consider a monopolist who sets the profit maximizing price. The monopolist does not have fixed costs. Marginal costs are MC = 3. The elasticity of demand at the profit
maximizing price is ELd = −2 (for your convenience I do not omit the minus sign here). What is
the profit maximizing price?
P = MC/(1-(1/ELd))
P = 3/(1-(1/-2)) = 6
The minimum wage in the U.S. was $1.50 in 1935 and $4.35 in 1998. The price index for 1935 was 34.2, and the price index for 1998 was 177.2. What is the difference between
the values of the minimum wages in terms of 1998 dollars (round to two digits)?
(1,50/34,2)*177.2 = 7.77
(4,35/177.5)*177.5 = 4.35
7.77 - 4.35 = 3.42
Consider a labor market for which the labor supply curve is given by LS (w) = 24w,
where w is the wage level. The labor demand curve is given by
LD (w) = 897 − 15w. Initially, the
market is in equilibrium. Then, there is a shock to the economy such that the labor demand changes to
LD (w) = 429−15w. The wage is downward rigid at the former equilibrium level. How
does the level of employment change?
Ls = Ld
24w = 897 - 15w
w = $23
Level of employment: 24(23) = 552
New level: 495 - 15(23) = 84
84 - 552 = - 468
Consider a monopolist with the cost function C(Q) = 4Q. Market demand is Q(P) = 48 - 2P. What is the deadweight loss from the monopoly?
Find MR, MC and D(inverse)
find the remaining values and do (b*h)/2
Consider a perfectly competitive market. Market demand is
Q(P) = 2451 - 4P.
All firms on the market are identical with cost function
C(q) = 20q^2 + 4q + 500
(q denotes the
production of the individual firm, Q is the market quantity produced by all firms together). How many firms will there be on the market in long-run equilibrium?
MC=40q + 4
ATC = 20q + 4 + 500/q
MC=ATC => q=5
P=MC => P= 40*5+4 = 204
Q=nq => Q=n5
Q= 2451 - 4204 =>
1635 => 1635=n5
n= 1635/5 => 327
The following curves are given
P(Q) = −100 Q + 12
S(P) = 300P
What is the deadweight loss occuring from a 2€ tax imposed on the buyer?
What is the income generated by the government?
Step 1 :
Inverse demand
find initial equilibrium:
1200 - 100P = 300P => P = 3
Solve Q : Q=300P => Q=900
Step 2:
Solve Q:
Q=300P => Q=3002,5 => Q=750
Step 3:
Actual new price: 2+2,5=4,5
Step 4:
DWL= 2(900-750)/2 = 150
Government Income: tax*Q = 1500
We are currently looking at a perfectly competitive
market for economics books. What is ourmaximized social surplus?
Buyers RV Sellers RV
Daniel 75 Eva 15
David 60 Erika 30
Diego 45 Elena 45
Dean 30 Elisabeth 60
Dax 15 Emily 75
Daniel and Eva = 60
David and Erika= 30
Diego and Elena = 0
==> 90
When the price of an energy drink is 1.50€, you decide to buy 8 energy drinks. When the price increases
to 2.00€ however, you decide to only buy 5 energy drinks. What is your price elasticity of demand for
energy drinks?
Price elasticity of demand =
Qnew - Qold
——————-
Qold
———————-
Price new - Price old
———————
Price old
==> -0,375/0,333 = -1,125
TC(q)=10000 + 100q^2
Q(P)=10000-P
Currently 300 producers.
How many producers will enter in long-run equilibrium
MC=ATC => q=10
P=MC => 10000-Q = 2000 => 8000/10
=800-300 => 500
Price floor
Price ceiling
above
below
Consider a perfectly competitive market. The demand curve is given by Q(P) = 119 - 6P and the supply curve is given by Q(P) = P. Consumption is taxed as follows: every consumer
must pay a tax of 7 Euro for every unit the consumer buys. What is the value of the deadweight loss?
Step 1
Qs=Qd <=> P=119-6P
=>7P=119 => P1 = 17 and Q1= 17
Step 2
Qd(P)=119-6(P+7) => P=119-6P-42
P2=11 and Q2=11
Step 3
Ptax= P2+tax = 11+7= 18
Step 4
DWL= (Ptax - P2)(Q1-Q2)/2
=> (18-11)(17-11)/2
= 21
Kevin wants to buy decoration for his Christmas tree and his budget is 20 Euro. He wants to buy candles and Christmas balls. Candles cost 50 cent a piece, Christmas balls cost 20 cent a piece. Before he decides how many to buy of each, he draws his budget constraint with candles on the vertical axis and Christmas balls on the horizontal axis. What is the slope of his budget constraint?
Y axis = 50
X axis = 20
slope of budget constraint
= -X-axis/Y-axis => -20/50 = -0,4
A monopoly faces market demand Q(P) = 120 - 0.1P and has the cost function C(Q) = 200Q + 15Q^2. What is the monopolist’s profit?
1) Find P = Inverse demand
=> P=1200-10Q
2) Revenue = P*Q
1200Q-10Q^2
3) Find MR=MC
1200-20Q=200-30Q => Q=20
Step 4
P=1200-10(20) = 1000
Step 5 profit
1200(10)-10(10^2) - 200(10)+ 15(10^2)
=10050
Suppose that labour supply is given by L(w) = 90 + 11w and labour demand is given by
Ld(w) = 2140 - 39w. Initially, the market is in equilibrium. Then, there is a shock to the economy such that the labor demand curve shifts to
Ld(w) = 1640 - 39w. How much involuntary unemployment is there after the shock if wages are downwardly
Ld - Ld(new) =
2160-39w-1640 - 39w = 500
U=X1*X2
Budget 100€
P1= 2€
P2= 2,5€
100 = 2X1+ 2,50X2
100 - 2,5X2/2 = X1
==>
(50 - 1,25X2)X2
(50X2 - 1,25X2)X2
(50X2 - 1,25*X2^2) = 0
50 - 2,5X2 = 0
==>
X2 = 20
X1 = 25
Real GDP of a country in 2016 was 120. In 2017, GDP deflator is 90 and GDP nominal is 144. What was real GDP growth in 2017?
GDP deflator =
(nominal GDP/real GDP) * 100
0,9 = 144/X
X = 144/0,9 = 160
Real GDP growth (RGG)
RGG = real GDP 2017 - real GDP 2016 –
RGG = 160-120/120 = 33%
year Px Qx Py Qy
1 10 150 20 100
2 20 250 40 240
3 30 350 50 300
Real GDP year 2 :
25010 + 24020 = 7300
Real GDP year 3 :
35010 + 30020 = 9500
===>
9500 - 7300/7300 = 30,1%
The current value of GDP is $16 trillion. The government is planning to increase spending by $960 million. According to the government’s calculations this spending increase will increase GDP by 12%. What is the value of the government expenditure multiplier in the government’s calculations?The current value of GDP is $16 trillion. The government is planning to increase spending by $960 million. According to the government’s calculations this spending increase will increase GDP by 12%. What is the value of the government expenditure multiplier in the government’s calculations?
1610^9
96010^6
1610^9 * 1,12 = 17,9210^9
17,9210^9 - 1610^9 = X96010^6
1,9210^9 = X960*10^6
1,9210^9/96010^6=x
x = 2
16*0,12 = 1,92
1,92/0,96 = 2
A picture was sold in 1950 for $110 and again in 2017, this time for $120. The consumer price index for 1950 was 8.7 and 15.6 for 2017. What was the difference in sales prices in terms of 2017 dollars (round to two decimals?
1995 2017
Price Index 8,7 15,6
Price 110 120
(Current PI/base PI) * value base
15,6/8,7 * 110 = 197,24
197,24 - 120 = 77,24
Tommy inherited 30,000 Euro in 1995. The price index for 1995 was 97, and the price index for 2021 is 188. What is the value of the inheritance in 2021 Euro?
(PI now/PI old) x inherent
(188/97) x 30000 = 58144
Poorland produces only two goods, good X and good Y. The following table shows the quantities produced and the prices in three different years. What was the inflation rate for year 2 (i.e., from year 1 to year 2), using the GDP deflator as price index and year 1 as base year (round to the nearest decimal if necessary)?
nominal year 2-real year 2/real year 2
Tommy inherited 30,000 Euro in 1995. The price index for 1995 was 97, and the price index for 2021 is 188. What is the value of the inheritance in 2021 Euro?
(Round to the nearest Euro.)
(PI now/PI old) x inheritance
(188/97) x 30000 = 58144
Consider a demand curve given by Q(P) = 36 - 14P. What is the price elasticity of demand at Q = 6?
D: Q(P) = 36 -14P
ELdemande= Q’(P).P/Q
6=36-14P <=> -30=-14P
P=2.143
Q=6
Q’(P)= -14
ELdemande= -14.2.143/6 = -5
A firm in a perfectly competitive market has the cost function
C(q) = 1,000 + 400Q + 200Q^2?
The short-run market price is given by P = 1,200. How much should the firm produce in the short run?
C(q) = 1000 + 400Q + 200Q^2
P = 1200
MC = 400 + 400Q
P=MC
==> 1200 = 400 + 400Q
=> Q = 2
Consider the market for bicycles. The demand curve in the northern part of the country is given by QN(P) = 20 - P while that in the southern part is Q(P) = 5 - 0.5P. Consider our
discussion of aggregate demand curves in the tutorials. Which of the following statements is correct?
(“Kink” here refers to a point on the demand curve (excluding the intersections with the x-axis and y-axis) at which the slope of the demand curve changes)
Qn(P) = 20 - P
Qs(D) = 5 - 0.5P
N+S = (20-P) + (5-0.5P)
=> 25 - 1.5P
=> 25 - 1.5P = P
P = 10
Consider our discussion of long run equilibrium in a perfectly competitive market. Which statement about the long run in a perfectly competitive market is correct?
- Free entry and exit of firms is no longer possible.
- Firms earn positive economic profits in equilibrium
- The long run supply curve is horizontal.
- Firms will produce positive quantities, but at less than efficient scale.
The long run supply curve is horizontal.
Contractionary fiscal policy leads to a
?
- leftward shift of the labor demand curve
- rightward shift of the labor demand curve
- leftward shift of the labor supply curve
- rightward shift of the labor supply curve
leftward shift of the labor demand curve
The GDP of Poorland is 2.5 million Euro. Government expenditures amount to 0.6 million Euro. The government considers decreasing its expenditures by 20%. Determine how this would change GDP, assuming that the government expenditure multiplier is 2.
(government expenditure)
*(% in decrease)/ exp. multiplier
= change GDP
0.6*(1-0.02)/2 = 24
Consider our discussion of different types of elasticities in class. Which of the following statements is ! NOT ! correct?
- Complements have negative cross-price elasticity, while substitutes have positive crossprice elasticity.
Normal goods have a negative income elasticity of demand, while inferior goods have a positive income elasticity of demand.
- As the number of available substitutes for a certain good grows, the price elasticity of demand for that good increases.
- Luxury goods such as foreign vacation are likely to have a high income elasticity of demand.
wrong : Normal goods have a negative income elasticity of demand, while inferior goods have a positive income elasticity of demand.
right : Normal goods have a POSITIVE income elasticity of demand, while inferior goods have a NEGATIVE income elasticity of demand.
