1. The following two linear functions represent a market (thus one is a supply f
ID: 1226978 • Letter: 1
Question
1. The following two linear functions represent a market (thus one is a supply function, the other a demand function). Circle the answer closest to being correct. Approximately what will the quantity demanded be if the government controls the market price to be $3.00 (You must first find the market equilibrium price and quantity in order to see how the $3.00 relates to them)?
Q = 100 – 4.6P and Q = 75 + 6.2P
2. There has been a change in the market (represented in 1 above). The change is represented by the following two equations. Circle the one correct conclusion that describes the market change.
Q = 65 + 6.2P and Q = 80 – 4.6P
3. Circle the function on the answer sheet that represents the marginal revenue (MR) function for this demand function: Q = 150 – 5P
4. Circle the quantity that maximizes total revenue (TR) for the marginal revenue (MR) function selected in number three (3).
5. If supply remains unchanged but demand increases, we can conclude that the new equilibrium:
Explanation / Answer
1. Assume
Demand function as 100-4.6p
Supply Function as 75+6.2p
The equation can be solved by,
4.6p=100
6.2p=75
By changing the sign we can solve this
4.6p=100 -
-6.2p=75
= -1.6p =25
Therefore p= 25/-1.6= 15.66
Thus price we take as 15.66
The equilibrium Quantity can be arrived by substituting p in any one of the equations:
100-4.6p
100-4.6*15.66 = 27.97
Thus Equilibrium price is 15.66, Equilibrium Quantity is 27.97
If we substitute $3 as p then,
100-4.6*3
100-13.8 = 86.2
Q.2)
Q= 65+6.2p can be taken as Demand Function
Q=80-4.6p can be taken as Supply function
To solve this:
6.2p= -65 -----------(1)
4.6p= -80-------------(2)
To solve this we change the sign of the equation (2)
6.2p = -65
-4.6p = 80
Answer:
1.6p = 15
Hence p = 15/1.6= 9.36
If we substitute p in Q=65+6.2p then,
Q= 65+6.2*9.36 = 123.03
Q.3)
Q=150-5p
MR=d(Q)/dp
= d(150-5p)/dp
= -5p-6
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