MICROECONOMICS EV Prof. Davide Vannoni. Exercise session 3 1.Firm in perfectly competitive market 2.Short-run and long-run competition 3.Price support

MICROECONOMICSEV

Prof. Davide Vannoni

Exercise session 3

1. Firm in perfectly competitive market

2. Short-run and long-run competition

3. Price support (see lecture slides)

4. Import quota (see lecture slides)

5. Gasoline Tax (see lecture slides)

Exercises

D. Vannoni e M. Piacenza

Microeconomia C, A.A. 2007-2008 Esercitazione 3

3

Exercise n. 1

Firm WWW (see exercise session 2) works in a perfectly competitive market, and bears the following costs:

Q.ty FC VC TC MC AVC AFC ATC

0 46 0 46 0 0 0 0

1 46 30 76 30 30 46 76

2 46 50 96 20 25 23 43

3 46 58 104 8 19,3 15,3 34,7

4 46 64 110 6 16 11,5 27,5

5 46 84 130 20 16,8 9,2 26

6 46 114 160 30 19 7,7 26,7

7 46 150 196 36 21,4 6,6 28

8 46 190 236 40 23,8 5,8 29,5

9 46 240 286 50 26,7 5,1 31,8

FC = fixed costsVC= var costsCT= tot costsMC= marginal c.

AC*=average c.** = V, F, T



4

a) If the price is 40 € compute: total revenues (TR), marginal revenue (MR) and profit.

Price Q.ty TC TR(PQ

)

MC MR (P)

Profit(MR –MC)

Profit(TR -TC)

0 46 0 0 0 0 -46

40 1 76 40 30 40 10 -36

40 2 96 80 20 40 20 -16

40 3 104 120 8 40 32 16

40 4 110 160 6 40 34 50

40 5 130 200 20 40 20 70

40 6 160 240 30 40 10 80

40 7 196 280 36 40 4 84

40 8 236 320 40 40 0 84

40 9 286 360 50 40 -10 74



5

a) Answer the following questions:

i. At which quantity profits are maximized?

The quantity in correspondence of which marginal revenue is equal to marginal cost (MR = MC), therefore Q = 8.

i. Which will be the profit (loss) at the above quantity?

Profit = Revenues – VC – FC

In correspondence of Q = 8, Profit = 320 –190 - 46= 84 €



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MC

P= MR

ATC

AVC

Profit



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i. How much will be the producer's surplus?

Producer's surplus = Revenues – VC

or

Surplus = Profit + FC = 84 + 36 = 130 €

i. Will the firm continue to produce in the long run?

Since the profit is positive, yes!



8

Notice

The producer's surplus can be measured

- as the difference between revenues and variable costs( PQ - QAVC ),

- as the sum, for all quantities up to that level, of the differences between price and marginal cost: look at the column Profit (MR –MC) : 10+20+32+34+20+10+4+0=130

(This is shown in the two following graphs)



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MC

P = MR

ATC

AVC

Producer's Surplus



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MC

P= MR

ATC

AVC

Producer's surplus



11

a) If the price reduces up to 20 €, which will be the profit maximizing quantity in the short run? What will happen in the long run?

The profit is maximized when MC= MR = P, that is in correspondence of MC = 20 €, i.e. for Q = 5.

Profit = 100 - 84 - 46= - 30 € (loss)

In the short run the firm is not making profits but reduces losses: since it cannot modify its structure (reason for which cost fixed exist), it continue to produce until (after recovering variable costs) there will be a positive margin to be used to partly recover fixed costs.



12

Recall the closure condition: AVC > P

- in the short run, the firm will continue to produce until the producer's surplus is positive.

- in the long run, all costs are variable; the firm will continue to produce only if the profit is positive.

In the long run, in our example, the firm will shut down!



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MC

P=MR

ATC

AVC

Loss



14

d) If the price reduces up to 15 €, which will be the profit (or the loss) in the case in which the firm will continue to produce? What should the firm do in the short run?

For p=15 € the optimal choice will be to produce 4 units (the maximum quantity for which MC<MR). Revenues will be lower than VC, and the difference (not recovered) will be added to the fixed costs.

By producing there will be a loss equal to: TR – (VC + FC) = 60 - ( 64 + 46 ) = - 50 €

The surplus will be negative: Profits + FC= - 50 + 46 = - 4 €

The firm in the short run will stop the production!



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Loss

Loss due to VC

MC

ATC

P=MR

AVC



16

Exercise n. 2

Consider a market in which there are 1000 consumers with demand pd= 8 - qd and 100 producers with the following cost

function TC= 10 + 2qs + (1/40) qs2.

a. Find the market equilibrium.

b. Compute the profits of producers and tell what will happen in a perfectly competitive market in the long run: what will be the price, the manufactured quantities, the profits?



17

a) To find the equilibrium we have to find the aggregate demand and supply functions.

pd = 8 – qd

qd = 8 – pd

Qd = qd = 8000 – 1000pd

Inverse demand function:

direct demand function:

Aggregating for1000 individuals:

The supply function coincides with the increasing portion of the MC which lies above the AVC:

Marginal Cost = C/ Q MC = 2 + (1/20) qs

Inverse supply: ps= 2 + 1/20 qs

Direct supply: qs = 20ps- 40



18

Aggregating for 100 firms: Qs=2000 ps - 4000

The market equilibrium is the price-quantity combination for which Qs= Qd 2000p - 4000 = 8000 - 1000 p

p* = 4Q* = 4000

qs* = 40 ; qd* = 4



19

a) Each producer earns a profit equal to:TR = 4 · (40) = 160TC = 10 + 2 · (40) + 1/40 · (402) = 130Profits = 30

The other firms will presumably enter the market attracted from the profit opportunities. The long run equilibrium is where the Marginal Cost equals the Average Cost.

MC = ATC 2 + 1/20 · q = (10 + 2·q + 1/40 · q2)/q

2 + 1/20 · q = 10/q + 2 + 1/40 · q

1 /40 · q = 10/q q2 = 400 q = 20 Each firm will therefore produce a quantity equal to 20 MC = ATC = 3



20

Since the price must equal the marginal cost, p = 3. The aggregate quantity bought on the market will be:

Qd = 8000 - 1000 · 3 = 5000

There will be 250 firms (5000/20); the profit will be TR – TC, therefore:

TR = 3 · 20 = 60

TC = 10 + 2 · 20 + 1/40 · 400 = 60

Profit = TR – TC = 0



21

P = 4

Aggregate Supply

4000 40008

8

404 Q Q

P P

Aggregate Demand

Individual Demand

Firm Supply

Graphically:

2



22

4000

3

8

4

Q

P

Aggregate Demand

5000

Aggregate Supply (before entry)

Due to the entry of new firms, the aggregate supply will be flatter and the equilibrium price reduces from 4 to 3; the quantity will be 5000:

Aggregate Supply(before entry)

2

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MICROECONOMICS EV Prof. Davide Vannoni. Exercise session 3 1.Firm in perfectly competitive market 2.Short-run and long-run competition 3.Price support