MANAGERIAL ECONOMICS OUEST?ONS 1. The following two linear functions represent a
ID: 2429450 • Letter: M
Question
MANAGERIAL ECONOMICS OUEST?ONS 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 equilibrium price be? 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-90-4.6P and Q 75+ 6.2P 3. Circle the function on the answer sheet that represents the marginal revenue (MR) function for this demand function: Q 90-4.6P 4. Circle the quantity that maximizes total revenue (TR) for the marginal revenue (MR) function selected in number three (3). 5. If supply increases and demand also increases, we can conclude that the new equilibrium:Explanation / Answer
(1) Price = 2.3
Equating demand and supply,
100 - 4.6P = 75 + 6.2P
10.8P = 25
P = 2.3
(2) (a)
The first equation shows an inverse relationship between price and quantity, so this is demand function. The second equation shows a direct relationship between price and quantity, so this is supply function. Here, the demand function has changed.
For initial demand function, when P = 0, Q = 100
For new demand function, when P = 0, Q = 90
Since vertical intercept of demand function has decreased, it means demand curve has shifted leftward due to a decrease in demand.
(3) (a)
Q = 90 - 4.6P
4.6P = 90 - Q
P = (90 - Q) / 4.6
Total revenue (TR) = P x Q = (90Q - Q2) / 4.6
MR = dTR/dQ = (90 - 2Q) / 4.6 = 19.57 - 0.44Q
(4) Q = 44.48
TR is maximized when dTR/dQ = 0, i.e. MR = 0
19.57 - 0.44Q = 0
0.44Q = 19.57
Q = 44.48
(5) (b)
Increase in demand shifts demand curve rightward, increasing price and increasing quantity. Increase in supply shifts supply curve rightward, decreasing price and increasing quantity. The net effect is a definite increase in quantity, but price may rise, fall or remain unchanged.
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