QUIZ 1
Name
Prob. 1 A minicomputer purchased at a cost of $60,000 in 1994 has a scrap value of $12,000 at the end of four years. If the straight-line method of depreciation is used:
a. Find the linear equation expressing the minicomputer's book value at the end of t years.
Let x be the number of years since the computer has been purchased
and y the book value of the computer at that time. Then, in year
zero the book value is $60,000 giving the point 
. In
four years the book value is $12,000, giving us the point 
. We know that the function which describes the depreciation
is linear so we use these two points to find the slope of the
function.
Using this slope and the point , we get the following
equation:
or
b. Find the minicomputer's book value at the end of the third year.
To find the book value of the computer after three years we plug three into this equation (for x) and get:
Prob. 2 The quantity demanded of a certain brand of videocassette recorder (VCR) is 3000 per week when the unit price is $485. For each decrease in unit price of $20 below $485, the quantity demanded increases by 250 units. The suppliers will not market any VCRs if the unit price is $300 or lower. But at a unit price of $525, they are willing to make available 2500 units in the market. The supply equation is also known to be linear.
a. Find the demand and supply equations.
We know that when the unit price is $485, 3000 VCR's will be sold. If the price decreases by $20 then the quantity demanded will increase by 250. If x is the quantity demanded and y is the price we have the two points (3000, 485) and (3250, 465). Using these points we get the slope
so the equation for the demand function is
or
Next, we have that if the unit price is $300 or less the no VCR's will be manufactured while if the unit price is $525, 2500 units will be manufactured. Thus, the supply function contains the two points (0,300) and (2500, 525). Since this function is linear it must have a slope of
and so the equation is
or
b. Find the equilibrium point.
The equilibrium point is simply the point at which the demand and supply equations intersect. In order to find the intersection point we set
Solving this equation for x we get:
To find the y value for the intersection point we solve the equation
Therefore, market equilibrium is achieved when the price is $525 and
the number of VCR's is 2500.