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 a supply curve

quantity supplied is directly related to price

60p +q - 940 =0

60p = 940-q

p = -q/60 + 37/3 is a demand curve

quantity demanded is inversely related to price

they're graphically two straight lines, one with y intercept = -20 and slope = 3/5, the other with y intercept 37/3 and slope =-1/60, nearly flat.

equilibrium price is when quantity supplied = quantity demanded

set the two equations equal and solve for q, then solve for p

-q/60 + 37/3 = .6q -20

.6q +q/60 = 37/3+20

37q/60 = 97/3

q = 97/3)(60/37)=1940/37

then plug that into either equation

to find equilibrium price

p=.6q -20 = .6(1940/37) -20 = 6(194)/37 -20 = 1164/37 -20 = 424/37 = about $11.46

a $5 subsidy shifts the supply curve up by 5

p=.6q -15

= -q/60 + 37/3

then

(.6 +1/60)q = 37/3 +15

37q/60 = 82/3

q= (82/3)(60/37) = 1640/37

p = .6(1640/37) -15

p= 984/37 -555/37= 429/37 = about $11.59