Word Problem Please need help with this asap

Question

Consider the following equations, where 𝑞 denotes quantity in thousands and 𝑝 denotes price in dollars:

0.6𝑞 − 𝑝 − 20 = 0

60𝑝 + 𝑞 − 940 = 0

1. Express 𝑝 as a function of 𝑞 in each of the above equations. Identify which is the supply and which is the demand function and briefly explain your reasoning.
2. Graph the supply and demand functions in the region 𝑞 ≥ 0, 𝑝 ≥ 0.
3. Find the equilibrium price and quantity in this market.
4. Suppose the government introduces a $5 subsidy (ie. opposite of a tax) to the supplier, find the new equilibrium price and quantity in this market.

Answer 1

.6q - p -20 = 0

p = .6q -20 is the supply curve. as price goes up, quantity supplied goes up Graphically, it's an upward sloping line

60p +q - 940 = 0

p = -q/60 + 15 2/3 is the demand curve. As price rises, quantity demanded goes down. Graphically, it's a slightly downward sloping line

set them equal to find the intersection point, the equilibrium price and quantity.

-q/60 + 15 2/3 = 6q/10 - 20

-q/60 + 47/3 = 36q/60 - 60/3

37q/60 = 107/3

q = (60/37)(107/3) = 20(107)/37 = about 57.8 thousand=about 57,800

p = 3q/5 -20 = 3(57.8)/5 -20 = 34.70-20 = about $14.70

$5 subsidy moves the supply curve vertically down by 5

from p = .6q -20, to

p=.6q -25

set that equal to the demand line to get

a new equilibrium price and quantity of

$14.60 and q=about 65.9 = about 65,900

the demand curve is relatively flat, slighly downward sloping, so the equilibrium price doesn't decrease that much.

It may help to graph the two lines

with the subsidy more quantity is supplied at a lower equilibrium price

it's as if the supply curve shifts right or downward

Answer 2

1) Add p to both sides: .6q - 20 = p

Add -q + 940 to both sides and divide by 60: p = (1/60)(940-q) Demand price goes down with quantity (2nd equation). For Supply price goes up.with quantity.

2) Graph the two lines.

3) In order to find the intersection, equate the two equations and solve for q

.6q-20 = 1/60 (940-q)

36q - 1200 = 940 - q

37q = 2140

q = 57.84 (x 1000) and p is .6(57.84) - 20 = 14.70

4) The supply is raised by an addition of 5 to the price. The equation becomes .6q - 15 = p and the analysis is the same in order to find the new equilibrium.

Please consider a tutor. Take care.