Stutz Department Store will buy 10 pairs of sunglasses if the price is $93 per pair and 30 pairs if the price is $43. The supplier of the sunglasses is willing to provide 35 pairs if the price is $98 per pair but only 5 pairs if the price is $38. Assuming that the supply and demand functions for the sunglasses are linear, find the market equilibrium point.

$68 for 20 pairs

Explanation:

Demand

$93 per pair for 10 pairs

$43 per pair for 30 pairs

Supply

$98 per pair for 35 pairs

$38 per pair for 5 pairs

Let x denotes price and y denotes a pair of sunglasses

x1, y1 = (93, 10)

x2, y2 = (43, 30)

x3 y3 = (98, 35)

x4, y4 = (38, 5)

Slope intercept form is given by

y = mx + b

m = y2 - y1/x2 - x1 = 30 - 10/43 - 93 = 20/-50 = -0.4

Now put any one x, y point from demand into slope equation to find b

30 = -0.4(43) + b

30 = -17.2 + b

b = 47.2

so the demand equation becomes

y = -0.4x + 47.2  eq. 1

Now for the supply equation

m = y4 - y3/x4 - x3 = 5 - 35/38 -98 = -30/-60 = 0.5

Now put any one x, y point from supply into slope equation to find b

5 = 0.5(38) + b

5 = 19 + b

b = -14

so the supply equation becomes

y = 0.5x - 14  eq. 2

Now we want to find the intersection of these two lines so that we can get the equilibrium point

-0.4x + 47.2 = 0.5x - 14

-0.4x - 0.5x + 47.2 + 14 = 0

-0.9x + 61.2 = 0

0.9x = 61.2

x = 61.2/0.9

x = 68

Now put it into eq. 1 or eq. 2

y = 0.5(68) - 14

y = 34 - 14

y = 20

So at market equilibrium the price of sunglasses is $68 for 20 pairs.

answer; ///i believe the correct answer is (c) laissez-faire;

the answer is "b.the increased supply will create a surplus. "

the essential thought behind price controls is straightforward - utilize the power of law to modify the equilibrium of a market. for instance, the legislature may choose that the steel business needs to survive, and in this way pass a law to set a value floor on steel. this implies all steel sold must offer at or over the floor value, which must be set over the equilibrium cost for it to have any impact. the switch could likewise happen - the administration can choose that steel is excessively costly and set a value roof underneath its equilibrium value, with the goal that all steel must be sold at or beneath that ceiling.