Question

Assume that the manufacturing of barbie doll is a perfectly competitive industry. The market demand for barbie doll is described by a linear demand

              function :

Qd = 6000 – 50P   ; P = price of a barbie doll.

                              9                    

           There are fifty manufacturers of barbie dolls. Each manufacturer has the same

             production costs given as TC(q) = 100 +q² + 10q ; q = quantity of barbie doll.     

1. Show that a firm in this industry maximizes profit by producing

q = (P -10) / 2. (Hint: use the profit-maximizing condition P= MC).

              

2. Show that equation of the industry supply curve (Qs) is equal to

25P – 250.

3. Find the market price and aggregate quantity traded in equilibrium.

4. How much does each firm produce?         

5. Show that each firm earns zero profit in equilibrium.

6. Calculate the competitive industry’s producer and consumer surplus.

7. Draw the graph of the industry demand and supply curve and indicate the area of consumer and producer surplus.                                  

Answer 1

(i)

Firm's MC = dc/dq = 2q + 10

For each firm, its supply curve is its MC, so

Firm supply curve: P = 2q + 10

2q = P - 10

q = (P - 10)/2

(ii)

Since there are 50 firms,

Market supply (Qs) = 50q

q = Qs/50

P = 2 x (Qs/50) + 10

P = (Qs/25) + 10

25P = Qs + 250

Qs = 25P - 250

(iii)

Equating Qd and Qs,

6000 - 50P = 25P - 250

75P = 6250

P = 8.33

Q = 6000 - 50 x 8.33 = 6000 - 416.5 = 5583.5

(iv)

Firm output = Market output / Number of firms = 5583.5 / 50 = 111.67