Question

1. A monopolist has variable costs of VC = q² and faces a demand curve of P = 24 – q, where P is price and q the quantity sold. If the monopolist sets a single price, what is its profit-maximising quantity?

a.2

b.4

c.6

d.8

e. none

2. A monopolist has variable costs of VC = q² and faces a demand curve of P = 24 – q, where P is price and q the quantity sold. If the monopolist sets a single price, what is the resulting loss in the gains from trade?

a.8

b.6

c.12

d.4

e.none

3. A monopolist has variable costs of VC = q² and faces a demand curve of P = 24 – q, where P is price and q the quantity sold. If the monopolist sets a single price what is profit (assume there are no fixed costs)?

a.48

b.64

c.72

d.36

e. none

4. A monopolist has variable costs of VC = q² and faces a demand curve of P = 24 – q, where P is price and q the quantity sold. If the monopolist engages in first-degree price discrimination, the resulting deadweight loss is?

a.6

b.16

c.32

d.64

e.0

5. A monopolist has variable costs of VC = q² and faces a demand curve of P = 24 – q, where P is price and q the quantity sold. (Consider that this demand curve is marginal benefit curve for an individual consumer.) The monopolist engages in first degree price discrimination using a two-part tariff, what is the fixed fee (F) and per-unit fee charged (p)?

a.F = 16, p = 8

b.F = 32, p = 16

c.F = 64, p = 8

d.F = 8, p = 4

e. none

Answer 1

Solution:

Given

monopolist variable costs of VC = q² and

faces a demand curve of P = 24 – q

1.If the monopolist sets a single price, what is its profit-maximising quantity is:

Option (c) is correct.

ie

$6

Calculation

VC = Q2

MC = dVC/dQ

MC = 2Q

P = 24 - Q

TR = PQ

= (24 - Q)Q

= 24Q - Q2

MR = dTR/dQ

= 24(1) -2Q

= 24 - 2Q

profit maximising condition is

MR = MC

24 -2Q = 2Q

2Q + 2Q = 24

Q = 24/4

Q = 6 units

2.If the monopolist sets a single price, what is the resulting loss in the gains from trade is:

Option (b) is correct.

ie

$6

Calculation

A monopolist produces where ,

Marginal revenue = marginal cost

Marginal revenue = d(total revenue)/d(q)

total revenue = price × quantity = q(24 - q)

Total revenue = 24q - q²

Marginal revenue = 24 - 2q

Marginal cost = d(total cost)/d(q)

Marginal cost = 2q

Put, marginal revenue = marginal cost

24 - 2q = 2q

24 = 4q

q = 24/4

quantity = q = 6

Price = 24 - q = 24 - 6 = $18

Competitive equilibrium:

In competitive equilibrium,

Price = marginal cost

24 - q = 2q

24 = 3q

q = 24/3

quantity = q = 8

Price = 24 - 8 = 16

It can be calculated as follows:

[(1/2)×(2)×(18-16)] + [(1/2)×(2)×(16-12)]

= 2 + 4

= $6

3. If the monopolist sets a single price profit (assume there are no fixed costs) is:

Option (c) is correct.

ie

$72

Calculation

At equilibrium in monopoly,

MR = MC

24-2q = 2q

24= 4q

So

Q* = 6

P = 24-6 = 18

So

profit = TR - TC

= 18*6 - 6*6

= 108-36

=72

4. If the monopolist engages in first-degree price discrimination, the resulting deadweight loss is:

Option (e) is correct

ie

$0

Calculation

In case of first degree price discrimination,

no deadweight loss exists,

bcoz Monopolist charges price till MC.

So full efficiency is restored, total surplus is still maximized.

5.The monopolist engages in first degree price discrimination using a two-part tariff, what is the fixed fee (F) and per-unit fee charged (p):

Option (b) is correct

ie

F = 32, p = 16

Calculation

In two part tariff ,

Optimal price = MC, &

fixed fee equals the consumer surplus at P= MC

So

MC = 2q

Thus at eqm ,

P= MC = 2q

24-q = 2q

24 = 3q

Q*= 8

Now

price = 2*8 = 16

Now ,

F = CS = .5*8*(24-16)

= .5*8*8

F = 32