Question

The research department of AMS SHINE Co. Ltd estimated that the supply function for their television sets is given by x r w s Qx  2000  3P  4P  P Where Px is the price of TV sets, Pr represents the price of a computer monitor, and Pw is the price of an input used to make televisions. Suppose TVs are sold for GH¢400 per unit, computer monitors are sold for GH¢100 per unit, and the price of an input is GH¢2000. (a) How many television sets are produced? (b) Drive and sketch the supply function (c) The Producer

Answer 1

The research department of AMS SHINE Co. Ltd estimated that the supply function for their television sets is given by

Supply Function:

Qx = 2000 + 3Px - 4Pr - Pw

Here, the Px, Pr and Pw values are given in the market.

Px = The price of TV sets

or, Px = GH¢ 400

Pr = The price of Computer Monitor

or, Pr = GH¢ 100

Pw = The price of an input

or, Pw = GH¢ 2000

Now, we will use the information to answer the following questions.

(a) From the supply function of Television is

Qx = 2000 + 3Px - 4Pr - Pw

Putting the values of Px, Pr and Pw from above we get,

Qx = 2000 + 3×400 - 4×100 - 2000

or, Qx* = 800

Hence, 800 television sets are produced.

(b) Now, let us put the values of Pr and Pw in the supply function, we get

Qx = 2000 + 3.Px - 4.Pr - Pw

or, Qx = 2000 + 3.Px - 4×10 - 2000

or, Qx = -400 + 3.Px.........(1)

The supply function for television is:

Qx = -400 + 3.Px.

The following diagram shows the supply function.

(c) The producer surplus is the area below the price level (i.e. Pw = 400) and above the supply curve. The producer surplus is labelled as triangle ∆ABC in the above diagram.

Hence, the area of triangle ∆ABC is the producer surplus. Hence,

Producer Surplus = ∆ABC

or, Producer Surplus = (1/2)×(400 - 400/3)×800

or, Producer Surplus = GH¢ 106666.67

Hence, Producer Surplus is GH¢ 106666.67.

Hope the solution is clear to you my friend.