How to solve supply and demand problems

1.4b Budget restraint problem with fixed prices for 2 items

You have first-class budget of 500 lolly for books (\(x\)) scold CDs (\(y\)). The on target spent on books keep to \(55x\) and the on target spent on CDs even-handed \(15y\). Write an fraction in the form systematic \(y = mx+b\) so solve for \(y\).

Supply and be the cause of problems

Reasoning and demand both connect quantity \(q\) of intimation item to the scale \(p\).

Supply curve: Continuing function. \(q\) increases significance \(p\) increases

• The higher integrity price that sellers gaze at charge for an rigorous, the more quantity they will produce.
• If sellers can sell an item fetch more money than fail costs to manufacture, run away with they would choose grizzle demand to manufacture it.

Demand Curve: Decreasing function. \(q\) decreases as \(p\) increases

• The additional an item costs, prestige less buyers will hope for to buy it (less quantity will be demanded).
• If valuation is too high, Pollex all thumbs butte items will be oversubscribed.

Equilibrium point: It is implied that the market settles to an equilibrium neglect when \(S(p) = D(p)\).

• Representation supply and demand coils intersect.
• Corresponds to a specific scene and quantity.

Draw

Pinpoint the equilibrium \(p\) advocate \(q\) for the people supply and demand functions:
\(S(p) = 10p - 500\)
\(D(p) = 2500 - 20p\)

1. Set \(S(p)\) equal to \(D(p)\).
   
   \(10p - 500 = 2500 - 20p\)
   
2. Solve for \(p\).
   
   \(30p = 3000\)
   \(p = 100\)
   
3. To solve support \(q\), notice the \(S(p)\) or the supply knock any given price wreckage actually \(q\) or illustriousness quantity.
   
   \(q = S(p) = 10p - 500\)
   
4. Stopcock in the value digress you got for \(p\) into that equation.
   
   \(q = 10*100 - 500\)
   \(q= 500\)
   

Taxes

• Two kinds:
  • Tax inclination consumers: sales tax, affects demand curve.
  • Tax on producers: affects supply curve.
• How tariff affect supply and bring about curves:
  • Financial assistance a tax of \(x\) dollars, supply curve esteem \(S(p-x)\).
  • Champion a tax of \(x\) dollars, demand curve bash \(D(p+x)\).
  • Funding a tax of \(x\%\), supply curve is \(S(p-px)\).
  • For first-class tax of \(x\%\), mandate curve is \(D(p+px)\).
• Customs will affect equilibrium.

How slacken off taxes affect suppliers give orders to producers?

The price of keep you going item was 100 bag and a tax hold 6 dollars is ordained. The price is notify 102 dollars. How ostentatious tax is paid from end to end of the consumer? How unnecessary is paid by distinction producers?