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Derived Demand, Joint Supply

 Derived Demand, Joint Supply

            The case of joint demand for producers’ goods is referred to as derived demand because the demand for any factor is a demand derived from the final product which that factor helps to produce. The demand for labour is a derived demand. It depends on the demand for the product it helps to make.

Marshall has defined workers who are jointly demanded with other factors would be successful in raising their wages (i) the demand for the services of that set of workers is inelastic (ii) the wage bill of this group forms a very small proportion of the total wage bill so that a rise in their wages does not substantially afflict the total cost of production of the commodity or (iv) if the other co-operant factors are squeezable i.e. the wages of the other workers are reducible or the suppliers of other factors are forced to accept low prices.

Joint Supply

            There are a number of products which have a common source of supply in that they are produced jointly. The production of one automatically involves the production of another, such as wool and mutton, wheat and straw, cotton and cotton seed etc. Joint products are also known as joint cost products.

            Joint products are of two types, first, whose proportions cannot be varied and second whose proportions can be varied. Products like wheat and straw or cotton or cotton seed is automatically amplified. But it is difficult to separate the cost of production of such products. Nevertheless, the price of each product can be fixed on the principle of ‘what the traffic will bear’ that is what the product will fetch in the market. In other terms, the price of each product will be determined by the marginal utility of each product to consumers. But the price of each product must be such that the sum of the revenues from their sale must equal their total cost of production.

Joint Products with Varied Proportions

            Let us consider if a Norway farmer wants to have more wool than mutton. He finds that a certain number of sheep of a specific breed yields more wool and less mutton. He obtains the surplus wool by extra expenditure of rearing the additional number of sheep. The extra cost of grazing is the marginal cost of wool. The price of each product will thus be determined by the equality of the marginal cost and the marginal utility of each product taken separately.

Now let us construct an illustration based on the above condition.

Illustration 1

            Let us assume if a Norway farmer’s outlay is $ 180 each to rear a sheep that yields 20 units of wool and 26 units of mutton, while another breed costs $160 each and yields 20 units of wool and 22 units of mutton. If he breeds 20 sheep of the first type and 22 sheep of the second type then what would be the marginal cost of a unit mutton?

Breed

No. of sheep

Units of wool

Units of Mutton

Total Cost

I

20

20x22 = 220

20x26 = 520

3600

II

22

22x20 = 220

22x22 = 484

3520

Difference per unit of mutton $2.2

 

---

36

80

Solution: 80 / 36 = $2.2

The marginal cost of a unit of mutton would be $2.2.

Similarly, for calculating the marginal cost of wool, we are assuming the following.

Illustration 2

Suppose he breeds two other varieties of sheep which cost the same per sheep, i.e. $ 180 and $160 each. He breeds 22 sheep of the first type and each sheep yields 20 units of wool and 22 units of mutton.

Breed

No. of sheep

Units of wool

Units of Mutton

Total Cost

I

22

22x22 = 484

22x26 = 572

3960

II

26

26x20 = 520

26x22 = 572

4160

Difference per unit of mutton $5.5

 

36

---

200

Solution: 200 / 36

The per unit marginal cost of wool would be $5.5

The co-relationship of the prices of such joint commodities whose proportions are variable is indicated in the below diagrammatic representation. WS is the marginal cost supply curve of wool and MS is the supply of mutton. Let DC be the original demand curve for the two products. As a result WQ is the quantity of wool sold is WP price. Assumed that the demand for wool rises, as indicated by upward shifting of the demand curve D to D1, it will raise the price of wool to WP1 and increase its supply to WQ1. However the increase in the supply of wool as a consequent of the higher demand price would not direct to a proportional increase in supply of mutton. The percentage hike in the supply of mutton would base wholesome on the extent to which the proportions amidst the two could be varied.

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