Please show the work so i can learn how this was solved. Thank you. The followin
ID: 1173663 • Letter: P
Question
Please show the work so i can learn how this was solved. Thank you.
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
2.3 84.3 86.2 89.3 93.1 93.6 (all close, but approximate)
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
a. demand has decreased
b. demand has increased
c. supply has decreased
d. supply has increased
e. supply has decreased and demand has decreased
f. supply has increased and demand has increased
3. Circle the function on the answer sheet that represents the marginal revenue (MR) function for this demand function: Q = 90 – 4.6P
a. MR = 19.57 - 0.44Q
b. MR = 21.74 - 0.44Q
c. MR = 26.09 - 0.44Q
d. MR = 33.33 - 0.66Q
e. MR = 30.00 -0.4Q
f. MR = 10.71 - 0.28Q
4. Circle the quantity that maximizes total revenue (TR) for the marginal revenue (MR) function selected in number three (3).
38.25 44.48 49.41 50.50 59.30 75.00
Explanation / Answer
1. Q=100-4.6P ( demand equation)
Q =75 + 6.2P ( Supply equation)
Equilibrium price: Qd = Qs
100 - 4.6 P = 75 + 6.2 P
25 = 10.8 P
P= 25/10.8 = $ 2.31
Hence, option(A) is correct.
2. Demand change to Q= 90- 4.6P
This change represents that the demand has decreased. Hence, optionA) is correct.
3. Q = 90- 4.6P
4.6 P= 90- Q
P = 19.57 - 0.22 Q
Total revenue , TR = PQ
= (19.57 - 0.22Q)Q
= 19.57 Q - 0.22Q2
Marginal revenue , MR= 19.57 - 0.44 Q
Hence, option(A) is correct.
4. Equate MR with 0, we get the quantity level that maximises total revenue,
19.57 - 0.44 Q =0
Q = 19.57/0.44 = 44.48