1.

The Zinger Company manufactures and sells a line of sewing machines.

Demand per period

(Q) for a particular model is given by the following relationship:

Q = 400

.5P

where P is price.

Total costs (including a "normal" return to the owners) of producing Q

units per period are:

TC = 20,000 + 50Q + 3Q

2

(a)

Express total profits (

) in terms of Q.

(b)

At what level of output are total profits maximized?

What price will be charged?

What

are total profits at this output level?

(c)

What model of market pricing has been assumed in this problem?

Justify your answer.

SOLUTION:

(a)

= (P

Q)

TC

P

= 800

2Q

= (800

2Q) Q

(20,000 + 50Q + 3Q

2

)

= 800Q

2Q

2

20,000

50Q

3Q

2

=

20,000 + 750Q

5Q

2

b)

Q

10

750

dQ

d

dQ

d

(condition for maximum

)

0 = 750

10Q*

Q* = 75 units/period

P* = 800

2(75) = $650/unit

* =

20,000 + 750(75)

5(75)

2

= $8125

(c)

Non-discriminating monopolist, since the demand curve has a steep negative slope

Hello dear, please I would like to understand the answer of part c of this question. Why did we refer to the demand curve and which is the slope?