Bicycle manufacturing

Despondent over the Red Sox's terrible season, Prof. Gruber decides to quit his day job and start a bicycle manufacturing firm in Kendall Square. As he starts looking into the bicycle manufacturing industry, he realizes it has some interesting features. First, he realizes that it operates as a competitive industry. Second, he finds that there are two technologies used by firms in the industry.

Technology 1 uses solar power, and has a cost function C¹(q)=q+4q²+32 for q>0. Technology 2 uses electricity from the grid and is more efficient, with a cost function C²(q)=q+2q²+32 for q>0. Assume that we are in the long run, so firms using both technologies can shut and leave the market at 0 cost, so that C(0)=0 for both technologies.

1.Compute the marginal cost for technology 1.

2.Compute the marginal cost for technology 2.

3.Compute the average cost for technology 1.

4.Compute the average cost for technology 2.

5.Derive the supply curve for each technology.

6.In the long-run, assuming that firms can choose their technology, what will happen?

Now let's pretend for a minute that only technology 2 exists. Suppose that market demand for bicycles is given by D(p)=82040p. Furthermore, assume that there is free entry for firms using technology 2.

7.What will be the long-run price in the market? p=

8.How much will each firm produce at this price? q=

9.What will the total number of firms be?

N=

Now, suppose that the government of Massachusetts offers solar subsidies to 10 bicycle manufacturers. These subsidies are for $80 and the manufacturers receive these subsidies as long as they construct a bicycle manufacturing plant using the newly-invented solar technology (i.e. technology 1).

10.Determine the new MC, AC, and supply curve for the solar technology with the subsidy.

The long run price, now that there are 10 bicycle manufacturers using technology 1, will remain at p=17. There is still free entry for firms using technology 2.

11.What quantity will be produced by each firm using technology 1? q1=

12.What quantity will be produced by each firm using technology 2?

q2=

13.In equilibrium, how many firms using technology 2 will there be in the market?

N2=

14.In equilibrium, how much profit will each technology 1 firm make? 1=

15.In equilibrium, how much profit will each technology 2 firm make?

2=

16.The long run aggregate supply curve in this market (i.e. the total amount supplied by all firms as a function of price) depends on whether the price is less than 17.

For p<17, Q^S(p)=

17.Now suppose that the State of Massachusetts increases the number of solar bike manufacturing subsidies it will give from 10 to 100. What is the new long-run price? p=

18.How much will be produced in total by firms with technology 1?

19.How much will be produced by total by firms with technology 2?

20.How many firms will there be with technology 1?

21.How many firms will there be with technology 2?

22.How much profit will be earned by each firm with technology 1? 1=

23.How much profit will be earned by each firm with technology 2?

2=