In: Economics
Can I get the answers to these with work shown? 2, 3, 4, and 5 only please.
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 $1.50 (You must first find the market equilibrium price and quantity in order to see how the $1.50 relates to them)?
Q = 100 – 4.6P and Q = 75 + 6.2P
Qd=100-4.6P Qs=75+6.2P P=$1.50
Qd=Qs 100-4.6P=75+6.2P = 25=10.8P P=2.31
P=1.50 Qd=100-4.6P =100-4.6(1.5) =100-6.9 =93.1
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 = 85 + 6.2P and Q = 100 – 4.6P
3. Circle the function on the answer sheet that represents the marginal revenue (MR) function for this demand function: Q = 100 – 3P
4. Circle the quantity that maximizes total revenue (TR) for the marginal revenue (MR) function selected in number three (3).
5. If supply decreases and demand also increases, we can conclude that the new equilibrium:
(2) Supply has increased but no change in demand
From demand function from part 1: When Q = 0, P = 100/4.6 = 21.7 (Vertical intercept)
From demand function from part 2: When Q = 0, P = 100/4.6 = 21.7 (Vertical intercept)
There is no change in vertical intercept which means demand curve didn't shift, so demand didn't change.
From supply function from part 1: When Q = 0, P = -75/6.2 = -12.1 (Vertical intercept)
From supply function from part 2: When Q = 0, P = -85/6.2 = -13.7 (Vertical intercept)
A decrease in vertical intercept means rightward shift in supply curve due to increase in supply.
(3)
Q = 100 - 3P
P = (100 - Q)/3 = 33.33 - 0.33Q
TR = P x Q = 33.33Q - 0.33Q2
MR = dTR/dQ = 33 - 0.66Q
(4)
Revenue is maximized when MR = 0
33 - 0.66Q = 0
0.66Q = 33
Q = 100
(5) Price increases and quantity is indeterminate
Decrease in supply shifts supply curve to left, increasing price and decreasing quantity. Increase in demand shifts demand curve to right, increasing price and increasing quantity. Net effect is definite increase in price but quantity is indeterminate.