The supplier will produce 1000 units if the selling price is

The supplier will produce 1000 units if the selling price is $20 per unit, and will produce 1500 units if the price is $25 per unit. What is the supply function?

Solution

The relationship between the quantity produced and offered for sale and the price reflects opportunity cost. Generally, it is assumed that there is a positive relationship between the price of the good and the quantity offered for sale.

Let the supply function be S(x) = y = ap + b, where y is the quantity produced and supplied, p is the price and a and b are constants. We are given that y = 1000, when p = 20 and y = 1500 when p = 25 so that 1000 = 20a + b …(1) and 1500 = 25a + b…(2) . On subtracting the 1^st equation from the 2^nd equation, we have 25a + b – 20a – b = 1500 – 1000 or, 5a = 500 so that a = 500/5 = 100. On substituting a = 100 in the 1^st equation, we get 20*100 + b = 1000 or, b = 1000 - 2000 = -1000. Thus, the supply function is S(x) = 100p - 1000