Answer to Question #188013 in Microeconomics for Addo Benjamin

Question

DBS Farms is a producer and retailer of farm products. DBS main products are Mangoes, Pawpaw and Pineapples. The current price of the Mangoes per Kilogram is GHS 50, the Pawpaw/Kg is GHS 80 and the Pineapple is GHS 40. This year the DBS Farms sold 10,000 kgs of Mangoes, 20,000 kgs of Pawpaw and 1 million kgs of Pineapples. In an attempt to improve revenue, the managers of the firm have decided to increase all prices by 10%. Market research has suggested that the price elasticity of demand for each product is: Mangoes: - 1.5; Pawpaw: -2.5; Pineapples: - 0.6. You have been asked to evaluate the planned price increases.

a. Comment on the planned price changes.

b. Would a 10% price reduction have been better for some or all of the products?

Answer 1

a.

Determination of new prices and the effect on sales (Demand) and eventually Total Revenue:

(i) Mangoes:

$\Delta$demand for mangoes = PED $\times$ $\Delta$P

= --1.5 $\times$0.1

= - 0.15

$\therefore$ New sales (demand) expected in kgs = 10,000 - (0.15 $\times$10,000)

= 8,500 kgs

(ii) Pawpaw:

$\Delta$ demand for pawpaw = PED $\times$$\Delta$ P

= - 2.5 $\times$0.1

= - 0.25

$\therefore$ New sales (demand) expected in kgs = 20,000 - (0.25$\times$20,000)

= (20,000 - 5,000)kgs

= 15,000 kgs

(iii) Pineapples:

$\Delta$demand for pineapples = PED $\times$ $\Delta$P

= -0.6 $\times$ 0.1

= -0.06

$\therefore$ New sales (demand) expected in kgs = 1,000,000 - (0.06 $\times$1,000,000)

= 1,000,000 - 60,000

= 940,000 kgs

effects of the price changes on Total Revenues

Current Total Revenue = GHS (50 $\times$10,000) + (80$\times$20,000) + (40$\times$1,000,000) = GHS 42.1Million

Expected Total Revenue after the planned price changes = (55$\times$8,500 ) + (88$\times$ 15,000) + (44$\times$ 940,000)

= GHS 43,147,500

Conclusion:

The planned price changes would adversely affect the demand (sales) of all the three commodities, although the revenue would rise a paltry by GHS 1,047,500 i.e. (43,147,500 - 42,100,000).

b.

Determination of new Demand (sales) had the prices been reduced by 10%

(i) $\Delta$demand for mangoes = PED $\times$ $\Delta$P

= --1.5 $\times$0.1

= 0.15

$\therefore$ New sales (demand) expected in kgs = 10,000 + (0.15 $\times$10,000)

= 11,500 kgs

(ii) Pawpaw:

$\Delta$ demand for pawpaw = PED $\times$$\Delta$ P

= 2.5 $\times$0.1

= 0.25

$\therefore$ New sales (demand) expected in kgs = 20,000 + (0.25$\times$20,000)

= (20,000 + 5,000) kgs

= 25,000 kgs

(iii) Pineapples:

$\Delta$demand for pineapples = PED $\times$ $\Delta$P

= 0.6 $\times$ 0.1

= 0.06

$\therefore$ New sales (demand) expected in kgs = 1,000,000 + (0.06 $\times$1,000,000)

= 1,000,000 + 60,000

= 1,060,000 kgs

Effects of the price reduction by 10% on Total Revenue:

Expected Total Revenue = (45$\times$ 11,500) + (72$\times$ 25,000) + (36$\times$ 1,060,000)

= GHS 43,776,000

Current Total Revenue: GHS 4,210,000

Conclusion:

Reducing the price by 10% would have been appropriated as it could lead to the rise in demand for all the commodities resulting in the rise in the total revenue by 1,676,000 from the current total revenue of GHS 42,100,000 to expected total revenue of GHS.43,776,000, although the change would not favor revenues generated from pineapples but the change is worth, altogether.