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

Question

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) 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?

b) 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?

Please show steps for question! Thank you

Explanation / Answer

a)

C = 6q + 0.01q2 + 100

MC = 6 +0.02q

supply curve is given by

p = MC  

p = 6 + 0.02q

p - 6 = q/50

50p - 300 = q

industry supply curve = nq

Qs = 10(50p - 300)

= 500p - 3000

Qd = 1800 - 100p

after imposition of tax new demand curve

Qd = 1800 - 100(p + t)

= 1800 - 100(p +1)

= 1800 - 100p - 100

= 1700 - 100p

short run euilibrium is given by

Qd =   Qs

1700 - 100p = 500p - 3000

4700 = 600p

p = 7.83

Q = 1700 - 100(7.83)

= 1700 - 783

= 917  

we have

p = 6 + 0.02q

7.83 = 6 + 0.02q

q = 91.5

C = 6(91.5) + 0.01(91.5)2 + 100

= 732.72

Profit = PQ - C

= 917(7.83) - 732.72

= 6447.39

since profit is positive so firm is not suffering by loss

b)

In LR

AC = MC =P

AC = C/q

=( 6q +0.01q2 + 100)/q

= 6 + 0.01q + 100/q

MC = 6 + 0.02q

AC = MC

6 + 0.01q + 100/q = 6 + 0.02q

100/q = 0.01q

q2 = 10000

q = 100

P = MC

MC = 6 + 0.02(100)

= 8

so P = 8

Qd = 1700 - 100p

= 1700 - 100(8)

= 1700 - 800

= 900

number of firms n = Q/q

= 900/100

= 9

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