# Linear pricing and the quality of goods

In this topic we consider a firm’s choice of linear price and goods quality.

The marginal revenue from an increase in quality, MRY, is the increase in revenue caused by a unit increase in quality:

MRY = = MRY =

1. Break even sales when the firm chooses both price and quality

Assume zero incremental fixed cost and cost has the ‘constant returns to scale’ form.

We consider the impact of a change in P accompanied by a change in Y. The change in P and Y causes a change in Q.  The change in P and Y will not change profit if:

(P– Y)Q

= (P+DP– Y -DY)(Q+DQ)

or:

0 = (P+DP– Y -DY)DQ +(DP-DY)Q

or:

=

The equation shows us the break even change in sales following a change in price DP and quality DY.

Note DY is an example of a DAVC discussed in topic 5.

1. Break even sales when the firm chooses both price and quality

Assume zero incremental fixed cost and cost has the ‘constant returns to scale’ form.

We consider the impact of a change in P accompanied by a change in Y. The change in P and Y causes a change in Q.  The change in P and Y will not change profit if:

(P– Y)Q

= (P+DP– Y -DY)(Q+DQ)

or:

0 = (P+DP– Y -DY)DQ +(DP-DY)Q

or:

=

The equation shows us the break even change in sales following a change in price DP and quality DY.

Note DY is an example of a DAVC discussed in topic 5.

1. Break even sales when the firm chooses both price and quality

Assume zero incremental fixed cost and cost has the ‘constant returns to scale’ form.

We consider the impact of a change in P accompanied by a change in Y. The change in P and Y causes a change in Q.  The change in P and Y will not change profit if:

(P– Y)Q

= (P+DP– Y -DY)(Q+DQ)

or:

0 = (P+DP– Y -DY)DQ +(DP-DY)Q

or:

=

The equation shows us the break even change in sales following a change in price DP and quality DY.

Note DY is an example of a DAVC discussed in topic 5.

Thus the marginal revenue from an increase in quality is:

MRY = Q……………………………………………………..

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