Question

4. Fuel is sold through local fuel stations under perfectly competitive conditions. All fuel stations owners face the same long – run average cost curve by AC = 0.01q – 1 +100/q and the same long – run marginal cost curve given by MC = 0.02q – 1 where q is the number of gallons sold per day.

1. i) Assume the market is in the long – run equilibrium, how much fuel will each individual owner sell per day?                                                                                         

ii) What are the long – run average cost and marginal cost at this output level?

2. The market demand for fuel is given by QD – 2,500,000 - 500,000P where QD is the number of gallons demanded per day and P is the price per gallon.
   1. Given your answer in part a, what will be the price of fuel in long – run equilibrium? How much fuel will be demanded?                                                     
   2. How many gas stations will there be?                                                

3. Suppose that because of the development of solar – powered cars, the market demand for fuel shifts inward to QD = 2,000,000 – 1,000,000P. In the long – run equilibrium, what will be the price of fuel? How much total Fuel will be demanded, and how many fuel stations will there be?

Answer 1

Ans.

a. i. Here we are considering long-run equilibrium in a perfectly competitive market and in the long run, all the firms in a perfectly competitive market earn zero profit and average cost becomes equal to marginal cost.

Hence long-run average cost (LAC)= long-run marginal cost (LMC)

0.01q-1+100/q = 0.02q-1

solving we get,

q= 100 gallons per day

hence, each individual owner will sell 100 gallons per day.

ii. To get long-run average cost and long-run marginal cost at this output level we put q=100 in the LAC and LMC equations.

Hence LAC = 0.01*100-1+100/100= 1

and LMC = 0.02*100-1 = 1

Hence, the long-run average and marginal cost will be equal to 1 at this output level

b. The market demand for fuel is given by QD = 2500000-500000P Where QD is the number of gallons demanded per day and in the long-run equilibrium price is equal to average cost and marginal cost so P= $1. So,

QD = 2500000-500000*1= 2000000 gallon

i. Hence the price of fuel in the long-run equilibrium will be $1 and 2000000 gallons will be demanded.

ii. Now each gas station is selling 100 gallons per day and 2000000 gallons will be demanded so there will be 20000 gas stations.

C. Now because of the development of solar-powered cars, the market demand for fuel shifts inward to QD= 2000000-1000000P, Now we know, P=$1, So, QD= 2000000-1000000=1000000 gallons.

So in the long-run equilibrium, 1000000 gallons will be demanded and each individual is selling 100 gallons per day and the er of fuel station declines to 10000.