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
Possible answers: 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 + 6.2P   and Q = 110 – 4.6P
Possible Answers: 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 = 75 – 7P
Possible Answers: a. MR=19.57-.044Q, b. MR=21.74-.044Q, c. MR=26.09-.044Q, d. MR=33.33-.066Q, 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).
Possible Answers: 38.25   44.48   49.41   50.50   59.30   75.00

5. If supply decreases but demand remains the same, we can conclude that the new equilibrium:
Possible Answers: a. Price must fall but market quantity is indeterminate.    b. Quantity must increase but market price is indeterminate.   c. Price must increase but market quantity is indeterminate.   d. Quantity must decrease but market price is indeterminate.   e. Price must increase and Quantity must increase.     f.   Price must increase and quantity must decrease.

Please show work on how you solved the questions.

Answer 1

(1)

In free market equilibrium, Demand = Supply.

100 - 4.6P = 75 + 6.2P

10.8P = 25

P = 2.31

So, a price of 3 is a floor price, at which

Quantity supplied = 75 + 6.2 x 3 = 75 + 18.6 = 93.6

(2) (f)

In demand function from part 1: When Q = 0, P = 100/4.6 = 21.7 (Vertical intercept)

In demand function from part 2: When Q = 0, P = 110/4.6 = 23.9 (Vertical intercept)

An increase in vertical intercept means rightward shift in demand curve due to increase in demand.

In supply function from part 1: When Q = 0, P = -75/6.2 = -12.1 (Vertical intercept)

In supply function from part 2: When Q = 0, P = -90/6.2 = -14.5 (Vertical intercept)

A decrease in vertical intercept means rightward shift in supply curve due to increase in supply.

(3) (f)

Q = 75 - 7P

P = (75 - Q)/7

TR = P x Q = (75Q - Q2)/7

MR = dTR/dQ = (75 - 2Q)/7 = 10.71 - 0.28Q

(4)

TR is maximized when MR = 0

10.71 = 0.28Q

Q = 38.25

(5) (f)

A decrease in supply causes a leftward shift in supply curve, which increases price and decreases quantity.