Question

You can sell 70 pet chias per week if they are marked at $1 each, but only 20 each week if they are marked at $2/chia. Your chia supplier is prepared to sell you 10 chias each week if they are marked at $1/chia, and 60 each week if they are marked at $2 per chia.

(a) Write down the associated linear demand and supply functions.

demand function

q(p) =

supply function	q(p) =

(b) At what price should the chias be marked so that there is neither a surplus nor a shortage of chias?

Answer 1

(a). Let the required linear demand function be d(p) = y = mx+b where y is the weekly demand for the no. of chias, x is the unit price, m is the slope and b is the y-intercept. Then m = (20-70)/(2-1) = -50 so that y = -50x +b. Further, y = 70 when x = 1 so that 70 = -50+b . Hence b = 70+50 = 120 and then the required linear demand function is d(p) = y = -50x +120.

Let the required linear supply function be s(p)= y = nx+c where y is the weekly supply of the no. of chias, x is the unit price, n is the slope and c is the y-intercept.Then n = (60-10)/(2-1) = 50 so that y= 50x +c. Further, y = 10 when x = 1, so that 10 = 50+c or, c = -40. Then the required linear supply function is s(p) =y = 50x -40.

(b). If there is an equilibrium, i.e. there is neither a surplus nor a shortage of chias, then d(p) = s(p) or,    -50x +120 = 50x -40 or, 100x = 160 so that x = $ 1.60. Thus, there will be neither a surplus nor a shortage of chias if the unit price is $ 1.60.