1. The following two linear functions represent a market (thus one is a supply f
ID: 1173499 • 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 suppliers willingly supply 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 = 90 + 6.2P and Q = 110 – 4.6P
3. Circle the function on the answer sheet that represents the marginal revenue (MR) function for this demand function: Q = 75 – 7P
4. Circle the quantity that maximizes total revenue (TR) for the marginal revenue (MR) function selected in number three (3).
5. If supply decreases but demand remains the same, we can conclude that the new equilibrium:
Explanation / Answer
1. The demand function is given as Q = 100 - 4.6P (this is the demand function as the slope of the demand curve (dP/dQ) is negative) and the supply function is given as Q = 75 + 6.2P (this is the supply function as the value of slope is positive).
At equilibrium, demand = supply
Or, 100 - 4.6P = 75+ 6.2P
Or, 10.8P = 25
Or, P = 25/10.8 = 2.32
At this price, equilibrium quantity demand = quantity supply = 100 - 4.6(25/10.8) = 89.35
If the government controls the market price to be $3 which is greater than equilibrium price, the suppliers will be willing to supply : Q = 75 + (6.2*3)= 93.6 units.
Therefore, at a price of $3, suppliers are willing to supply 93.6 units which is greater than the equilibrium quantity supply.
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