Question: exercise 145 phillips industries manufactures a certain product that can...

Exercise 14.5

Phillips Industries manufactures a certain product that can be sold directly to retail outlets or to the Superior Company for further processing and eventual sale as a completely different product. The demand function for each of these markets is

Retail Outlets: P1=120−Q1Retail Outlets: P1=120−Q1

Superior Company: P2=40−Q2Superior Company: P2=40−Q2

where P1P1 and P2P2 are the prices charged and Q1Q1 and Q2Q2 are the quantities sold in the respective markets. Phillips’ total cost function for the manufacture of this product is

TC=10+8(Q1+Q2)TC=10+8(Q1+Q2)

What is Phillips’ total profit function?

119Q1−Q12+30Q2−Q22−10119Q1−Q12+30Q2−Q22−10

112Q1−Q12+32Q2−Q22−10112Q1−Q12+32Q2−Q22−10

120Q1−Q12+40Q2−Q22−10120Q1−Q12+40Q2−Q22−10

112Q1−Q12+32Q2−Q22112Q1−Q12+32Q2−Q22

The profit-maximizing levels of price and output for the retail outlets market are

per unit and

units respectively.The profit-maximizing levels of price and output for the Superior company are

per unit and

units respectively.At these levels of output, the marginal revenue in the retail outlets market is

and the marginal revenue in the Superior Company market is

.What are the total profits if Phillips is effectively able to charge different prices in the two markets?

.If Phillips is required by law to charge the same per unit in each market, the profit-maximizing level of price and output are

per unit and

units, respectively. Total profits in this condition are

.