Please fill in all missing blanks a) The demand for a certain product is given b
ID: 3203401 • Letter: P
Question
Please fill in all missing blanks
a)
The demand for a certain product is given by p+2q equals =362, and the supply for this product is given by
p2q=238, where p is the price and q is the number of products. Complete parts (a) and (b) below.
a. Find the price at which the quantity demanded equals the quantity supplied. $_______
b. Find the equilibrium quantity.______
b)
A retail chain will buy 900 cordless phones if the price is $20 each and 500 if the price is $60. A wholesaler will supply 350 phones at $30 each 1750 at $70 each. Assuming that the supply and demand functions are linear, find the market equilibrium point and explain what it means.
Market equilibrium occurs when the number of units is______ and the price is $______ per unit.
The relationship between the length of a pendulum L and the time L (ft) TT (sec) T for one complete oscillation can be determined from the data in 1.0 1.13 the table to the right. 1.5 1 36 2.0 1.57 a. Find the least squares line equation and graph it simultaneously 1.76 with the data points, with L as the horizontal axis and T as the 3.0 1.92 vertical axis. Does it seem to fit the data? 3.5 2.08 b. Find the correlation coefficient and interpret it. Does it confirm your answer to part a?Explanation / Answer
a) Demand for a product: p + 2q = 362
Supply for a product: p - 2q = 238
p is the price and q is the number of products
a Quantity demanded = Quantity supplied
This means that Demand and Supply of the product will intersect at a common point, meaning that both the demand and supply will have the same p and the same q value.
Therefore, we can treat the equations ( p + 2q = 362 and p - 2q = 238) as simultaneous equations.
p + 2q = 362 .....i
p - 2q = 238.......ii
Adding the two equations, we get the following:
2p = 362 + 238 = 600............ (q gets cancelled)
Therefore p = 600/2 = 300
b Using p = 300 in any of the given equations (i or ii), we get the following
p + 2q = 362
If p = 300, 300 + 2q = 362,
2q = 362-300 = 62,
q = 31
Therefore a) equilibrium price is $300 and a) equilibrium quantity is 31
b)Suppose the demand function is the following
qd = ad + bdpd ............................iii
where ad is the intercept, bd is the slope, qd is the quantity demand andpd its the price for that quantity
And the supply function is the following
qs = as + bsps ............................iv
where as is the intercept, bs is the slope , qs is the quantity demand andps its the price for that quantity
Now applying the data to the demand function, we get
900 = ad + 20bd and 500 = ad + 60bd
Solving the above is simultaneous equation, we get the following
900 = ad + 20bd
(-)500 = ad + 60bd
400 = -40bd,
Therefore, bd = -10 and ad = 900 - 20bd or 500 - 60bd = 900 + 200 or 500 + 600
Therefore ad = 1100
Thus the demand function is qd = 1100-10pd ................v
To repeat the same for the supply function
We apply the data to the supply function, we get
350 = as + 30bs and 1750 = as + 70bs
Solving the above is simultaneous equation, we get the following
1750 = as + 70bs
(-)350 = as + 30bs
1400 = 40bs,
Therefore, bs =35 and as = 1750 - 70bs or 350 - 30bs = 1750 - 2450 or 350 - 1050
Therefore as = -700
Thus the supply function is qs = -700 + 35ps ................vi
There is market equilibrium when demand and supply quantity is the same and so is the price, therefore,
qs = qd = qand ps = pd = p
Applying that in equation v and vi, we get
q = 1100-10p and q = -700 + 35p
Solving these as simultaneous equations, we get the following
q = 1100-10p
(-)q = -700 + 35p
0 = 1800 - 45p,
45p = 1800, p = 40, q = 1100-10p or -700 + 35p
q = 1100-10*40 or -700 + 35*40
= 1100-400 or -700 + 1400
= 700
Therefore, market equilibrium occurs when number of units is 700 and price is $ 40