# Math Help - supply, demand and price equilibrium in perfect competitive market

1. ## supply, demand and price equilibrium in perfect competitive market

" The Market for good X is perfectly competitive. the demand and supply functions of good X are given as follows:
Qd= 6000 - 30P
Qs= -500 +20 P

Where Qd is quantity demanded in thousands units, Qs is quantity supplied in thousands units, and P is the price in dollars for good X. All firms in the market are identical. The market is in long-run equilibrium and there are 1,000 firms producing good X under thsi initial long-run equilibrium.

a) What are the equilibrium market price and market quantity for good X?
b) what is the out put of each firm in the initial long-run equilibrium?

Now suppose the government gives an $8 per-unit subsidy to the consumers for each unit of good X consumed. c) after the provision of the per-unit subsidy to the consumers, what are the short-run equilibrium market price and market quantity for good X? d) Out of the$8 per-unit subsidy to the consumers, what are the short-run equilibrium market price and market quantity for good X?
e) What are the long-run equilibrium market price and market quantity for good X?
f) Out of the $8 per-unit subsidy of good X, how much is the share received by the consumers in the long run? g) Explain whether the number of firms in the new long-run equilibrium is larger or smaller than 1,000 and whether the new long-run equilibrium market output is larger or smaller than the initial level. " 2. Solve Qd = Qs? Surely this will get you started. 3. Ya.. i got the part a & b, but now, when the government gives an$8 per-unit subsidy, which mean the demand curve will shift right, thus the equilibrium price & demand will increase. but How much??? don't know how to calculate it.. with the given info...

4. What's "P"?

If the government pays the first $8, isn't that now "P-8" to the consumer? 5. I don't think it works that way.... casue government provide subsidy to consumer.. more consumer will demand for the product X .. that there will be increase in demand. if the demand increase the price will go up as well as the supply will go up..... increase in both demand & supply & price... 6. That's what I said. Compare Unsubsidized Qd= 6000 - 30P Qs= -500 +20 P vs. Subsidized Qd= 6000 - 30(P-8) Qs= -500 +20 (P-8) 7. Thank You So much TKHunny I really appreciate your help.... it's very helpful to me.... Thank again... Khun Aung 8. Hi,, here is what i got... At equilibrium, Qd=Qs 6000-30P=-500+20P P=130 Therefore Qd=6000-30(130)=2100 Qs=-500+20(130)=2100$8 per-unit subsidy to consumers D move to D’ but the supply curve remain unchange

We need to find the equation of the new demand curve ( D’)
now P=138

Qd =2100= Y-30(138)
Y=6240

the equation for new demand cruve is Qd'=6240-30P

at equalibrium Qd'=Qs

6240-30Pe=-500+20Pe
Pe=134.8

Qd=Qs=Qe=2196*1000= 2,196,000 units

Plz refer to the graph...