In a local agricultural market, there are 25 identical cassava producers operating under c… — JAMB UTME

In a local agricultural market, there are $25$ identical cassava producers operating under competitive conditions. The individual supply function for each producer is expressed as $Q_i = -15 + 4P$ , where $Q_i$ represents the quantity supplied by a single producer in bags and $P$ is the market price per bag in Naira ( $\text{₦}$ ). If the total aggregate market quantity supplied is $1,325$ bags, what is the prevailing market price per bag in Naira?

Answer: 17 Naira

Answer

The prevailing market price per bag is ₦17.

To calculate the prevailing market price, aggregate individual producer supply into the market supply equation by multiplying by the total number of producers:

Q_M = 25 \times (-15 + 4P) = -375 + 100P

. Substituting the market output of

1,325

bags gives

1325 = -375 + 100P

. Rearranging terms results in

100P = 1700

, which gives

P = 17

Naira.

Step-by-Step Solution

Aggregate individual producer supply functions to find the total market supply equation.

Q_M = 25 \times (-15 + 4P) = -375 + 100P

Market supply is the horizontal summation of all individual producers' supply functions in a competitive market.

Substitute the total market quantity supplied into the market supply equation.

1325 = -375 + 100P

The aggregate market quantity supplied is given as 1,325 bags.

Isolate the price variable P to compute the market price.

P = 17

Adding 375 to both sides yields

100P = 1700

, and dividing by 100 gives

P = 17

Naira.

Key Concept

Aggregation of Individual Supply Functions to Derive Market Supply

Estimated Time:2m 0s

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