Microeconomics 214 / Mikro ekonomie 214
Tutorial 5 / Tutoriaal 5
This tutorial is provided on SunLearn with the answers due to the public holiday next week and
that the tut for certain students falls on the public holiday. / Die tutoriaal word op SunLearn
geplaas met die antwoorde weens die publieke vakansiedag volgende week en die feit dat sekere
studente se tutperiode op die vakansiedag val.
1.
Suppose production processes X and Y give rise to the following marginal and average
cost curves: / Gestel produksieprosesse X en Y gee aanleiding tot die volgende
marginale en gemiddelde kostekurwes:
MCX = 18QX
𝐴𝑇𝐶𝑋 =
24
𝑄𝑋
+ 9𝑄𝑋
MCY = 6QY
𝐴𝑇𝐶𝑌 =
360
𝑄𝑌
+ 3𝑄𝑌
where the subscripts denote production processes X and Y respectively. / waar die
onderskrifte produksieprosesse X en Y impliseer.
What is the cheapest way to produce 48 units of output? / Wat is die goedkoopste
metode om 48 eenhede uitset te produseer?
2.
Rassie Erasmus Ltd is the only supplier of miniature world cups to the South African
rugby supporters. The demand curve for these world cups is given by P = 180 – Q.
The marginal cost of producing a world cup is constant at R30 per cup. / Rassie
Erasmus Bpk is die enigste verskaffer van minuatuur wêreldbekers aan die SuidAfrikaanse rugby ondersteuners. Die vraagkurwe vir hierdie wêreldbekers word
gegee deur P = 180 – Q. Die marginale koste om beker te produseer is konstant teen
R30 per beker.
What is the profit-maximising quantity, price and total revenue earned by Rassie
Erasmus Ltd? / Wat is die winsmaksimerende hoeveelheid, prys en totale inkome
verdien deur Rassie Erasmus Bpk?
3.
If the market demand curve facing Bertrand duopolists is given by P = 88 – 2Q, and
each has a constant marginal cost of R40/unit, what will the equilibrium price and
quantity for each firm be? / Indien die markvraagkurwe wat Bertrand duopoliste
konfronteer gegee word deur P = 88 – 2Q, en elkeen ’n konstante marginale koste
van R40/eenheid het, wat is die ewewigsprys en –hoeveelheid vir elke firma?
4.
If the market demand facing two Cournot duopolists is given by P = 128 – 4Q, and
each has a constant marginal cost of R80 per unit, what will be the equilibrium price
and quantity for each firm? / Indien die markvraagkurwe wat twee Cournot duopoliste
konfronteer gegee word deur P = 128 – 4Q, en elke firma ‘n konstante marginale
koste van R80 per eenheid het, wat sal die ewewigsprys en ewewigshoeveelheid van
elke firma wees?
5. Carlos Grootmeneer Ltd is a firm in the tennis racket industry and it act as the dominant
price leader in the industry. The market demand is given by PM = 800 – Q. The
combined supply by the smaller firms is PS = 400 + Q. The marginal cost curve of
Grootbek Ltd is given by MCDOM = 198 + 2Q. What will be the price in this industry,
what quantity will be traded in this market and how is that quantity split up between
Grootbek Ltd and the smaller firms? / Carlos Grootmeneer Bpk is ‘n firma in die
tennisraket -bedryf en tree op as die dominante prysleier in hierdie industrie. Die
markvraagkurwe word gegee deur PM = 800 – Q. Die gekombineerde aanbod van die
kleiner firmas word gegee as PS = 400 + Q. Die marginale koste van Grootbek Bpk is
MCDOM = 198 + 2Q. Wat sal die prys in hierdie industrie wees, hoeveel eenhede sal in
die mark verhandel word en hoe sal hierdie hoeveelheid tussen Grootbek Bpk en die
Kleiner firmas verdeel word?
MEMO
Vraag 1
Cheapest where MCX = 18QX = MCY = 6QY
Gegee QX + QY = 48; so QY = 48 - QX
Therefore 18QX = 6(48 – QX) = 288 – 6QX
So QX = 12
QY = 48 -12 = 36
ATCX = (24/12) + 9(12) = 110 ; ATCY = (360/36) + 3(36) = 118
TCX = 110 x 12 = 1 320
TCY = 118 x 36 = 4 248
TC = 5 568
Question 2
P = 180 – Q and MC = 30
So MR = 180 – 2Q
Eq: 180 – 2Q = 30
So Q = 75
P = 180 – 75
= 105
TR = 105 x 75
= 7 875
Vraag 3
P↓ to P = MC
So 88 – 2Q = 40
Q = 24
Both firms Q = 24 en P = 40
Question 4
P = 128 – 4Q, MC = R80
P1 = (128 – 4Q2) – 4Q1
TR1 = (128 – 4Q2)Q1 – 4Q12
MR1 = 128 - 4Q2 – 8Q1 = 80 = MC
Q1* = 6 - ½Q2 ; so Q2* = 6 - ½Q1
Eq: Q1* = 6 - ½Q2 = Q2* = 6 - ½Q1
So 3/2Q1 = 6; Q1 = 4
Also Q2 = 4
P = 128 – 4(4 + 4) = 96
Vraag 5
Market: PM = 800 – Q; so Q = 800 - P
Small Firms: PSF = 4mm00 + Q; Q = P - 400
Where PM = 800 – Q = PSF = 400 + Q
Q = 200 and P = 600
Where SupplySF =0 is Q = 400
QDOM = QM – QSF
= 800 – P – (P – 400) = 1 200 – 2P
So PDOM = [(1200-Q)/2] = 600 - ½Q
MRDOM = 600 - Q
Eq for dominanr firm: MR = MC
600 – Q = 198 + 2Q
QDOM = 134
PDOM = 600 - ½(134) = 533
PSF: 533 = 400 + Q = 133
QTOTAL = 135 + 133 = 267