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Short and long run equilibrium analysis

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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) What is the short run market supply curve?

(b) What will be the equilibrium price and volume of bread sales in the market?

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

(d) 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?

(e) 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?

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Solution describes the steps for finding short run equilibrium volumes and prices for identical bakeries. It also analyses the impact of tax on loaf of bread.

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Solution:

(a) What is the short run market supply curve?

Ci = 6qi + 0.01qi2 + 100
Marginal Cost = MCi = dCi/dqi =6+0.02qi
In perfect competition p=MC
p=6+0.02qi
0.02qi=-6+p
qi = -300+50p
Market supply curve
Q=10*qi=10*(-300+50p)=-3000+500p
Qs=-3000+500p

(b) What will be the equilibrium price and volume of bread sales in the market?

Qd=1800-100p
Qs=-3000+500p
For equilibrium Qd=Qs
1800-100p=-3000+500p
600p=4800
p=8

Qd=1800-100*8=1000
Qs=-3000+500*8=1000

Equilibrium price =$8

Equilibrium quantity = 1000

(c) At the equilibrium of (b) ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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