Q2. Currently 10 identical bakeries are producing bread in a competitive market.

Question

Q2. Currently 10 identical bakeries are producing bread in a competitive market. The cost           function for a typical bakery is:

                         Ci = 6qi + 0.01qi2 + 100.

The demand for bread is:

                          q = 1800 - 100p

(a) At the equilibrium of (b) what is the output per bakery? Are bakeries incurring losses, making profits, or breaking even?

(b) The government imposes a $1 per loaf tax on bread (let them eat cake!). In the short

run what will be market volume and price, and output per bakery? Will individual

bakeries suffer a short-run loss, and if so, how much?

(c) What will be the long run response of market price and volume to imposition of the $1 per loaf tax? How many bakeries will remain, and what will be output per bakery?

Explanation / Answer

1. To find the output produced by each individual bakery, we need to find out the total quantity demanded in the market. We are given that total quantity demanded, Qd = 1800 – 100p and,

Number of firms= 10.

So, total output produced by each bakery will be = Qd /10 or, = (1800 – 100p)/10

Step 1: Finding Qd, Qs, qi+ and P

At equilibrium we know, quantity demanded is equal to quantity supplied

Thus, Qd = Qs-----------------eq(1)

Qs is the market supply curve which can be found out using individual firm supply curve,

Qs = 10qi……………..eq(2)

Where, qi is the individual firm supply curve. To find qi , we need to use the P=MC condition for equilibrium.

P = MCi

(MCi is the marginal cost for each individual firm)

We have, cost function for a typical bakery as:

Ci = 6qi + 0.01qi2 + 100.

Thus, MC(q) = dC(qi)/dq = 6 + 0.02qi

Or, P = 6 + 0.02qi

Or, P/0.02 = (6/0.02)+ qi …………..(Dividing all terms by qi)

Or, 50P = 300 + qi

Thus, qi = 50P-300……………….eq(3)

Now using equations 2 and 3

Qs = 10(50P-300) = 500P-3000

Now using equations 2 and 3

Qd = 500P-3000

Or, 1800 – 100p = 500P-3000

Or, 600P =4800

Or, P= $8

Thus, Qd = 500P-3000 = 500(8)-3000 = 1000 units

So, total output produced by each bakery will be = 1000/10 = 100 units

Now, each firm’s profit is given by:

= Pqi – [6qi + 0.01qi2 + 100]

=8*100-[6*100+0.01*1002+100]

=0

Hence, the bakeries are breaking even with no profit or loss.
2.

The tax imposed is per loaf based hence it will act as a variable cost. Thus as per the same logic in part 1 we will find the answers for output, profit and Price.

Qs = 10qi

Where, qi is the individual firm supply curve. To find qi , we need to use the P=MC condition for equilibrium.

P = MCi

(MCi is the marginal cost for each individual firm)

We have, cost function for a typical bakery as:

Ci = 6qi + 0.01qi2 + 100 +qi (This is additional variable cost bceuase of tax imposed)

Thus, MC(q) = dC(qi)/dq = 7+ 0.02qi

Or, P = 7 + 0.02qi

Or, P/0.02 = (7/0.02)+ qi …………..(Dividing all terms by qi)

Thus, qi = 50P-350

Now Qs = 10(50P-350) = 500P-3500

Qd = 500P-3500

Or, 1800 – 100p = 500P-3500

Or, 600P =5300

Or, P= $8.83

Thus, Qd = 500P-3500 = 500(8.83)-3500 = 916.7 units

So, total output produced by each bakery will be = 916.7/10 = 91.6 units

Now, each firm’s profit is given by:

= Pqi – [7qi + 0.01qi2 + 100]

=8.83*91.67-[7*91.67+0.01*91.672+100]

= -$16

Hence, the bakeries are incurring a loss of $16 on imposing a $1 tax.

3.

Ci= [7qi + 0.01qi2 + 100]

In the long run this would be equal to minimum of average cost

Thus, ACi= [7qi + 0.01qi2 + 100]/qi

= 7 + 0.01qi + (100/qi)

ACi/qi= 0.01 - (100/qi2) =0

Thus qi= 100 Units

And ACi = 7+0.01(100)+(100/100) = $ 9

Thus Output= 1800-100P

Qd = 1800- 100(9) = 900 units

Now, the output in the long run comes to be 900 units and the individual demand qi was found to be 100 units above. Thus the number of firms that would remain is = Qd/ qi = 900/100= 9

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