Answer to Question #270261 in Calculus for mimi

Question

The quantity demanded per month of a product is 250 units when the unit price is Ksh 1400. The quantity demanded per month of the same product is 1000 when the unit price is Ksh 1100. The quantity suppliers will supply to the market is 750 units when the unit price is Ksh 600 or lower and will supply 2250 units if the price is Ksh 800. Both the Supply and Demand functions are known to be linear. Required

: i. Find the demand function (2 marks)

ii.Find the supply function (2 marks)

iii. find the equilibrium price and quantity (4 marks)

Answer 1

a.

$y=mx+c$

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{1100-400}{1000-250}=\frac{-2}{5}$

so our demand function becomes

$y=\frac{-2}{5}x+b\\1400=\frac{-2}{5}(250)+b\\1500=b$

demand function

$=p=\frac{-2}{5}x+1500$

b.

supply function given by two points (750, 6000) +(2250, 800)

$m=\frac{800-600}{2250-750}=\frac{200}{1500}=\frac{2}{15}$

$y=\frac{2}{15}x+c\\600=\frac{2}{15}(750)+b\\500=b\\$

supply function $p=\frac{2}{15}x+500$

c

$\frac{2}{5}x+1500=\frac{2}{15}x+500\\1000=\frac{Q}{15}x\\Q=1275 \space units$

$p=\frac{2}{15}x+500\\p=750\space kshs$