Economics notes on market equilibrium

Finding the market equilibrium:

Graphically  -- check out this prior post on finding market equilibrium graphically.

Mathematically – information with examples about finding market equilibrium mathematically.

Here is another example:

Begin with the implicit demand function for bacon: Q_d=D(p, p_b, p_c, Y)

Then you are given the explicit demand function for bacon: Q_d=171-20p+20p_b+3p_c+2Y

1. Where Q_d is million kilograms of bacon demanded annually, Y is thousands of dollars, and p, p_b ­(the price of bread), and p_c (the price of cantaloupe) are in dollars.
2. Assuming p_b, p_c, and Y are 4, 3 1/3, and 12 1/2 gives:
3. Q_d=171-20p+(20*4)+(3* 3 1/3) + (2*12 1/2)
4. Q_d = 286-20p

Implicit supply function for bacon: Q_s=S(p,p_h)

Explicit supply function for bacon: Q_s=178+40p-60p_h

1. Assuming 1.5 for p_h (the price of hogs) gives:
2. Q_s=178+40p-(60*1.5)
3. Q_s=88+40p

Just like in the graphical example, we solve where they are equal, so we equate Q_s and Q_d, this gives us:

1. Q­_d = 286-20p=88+40p = Q_­s­
2. 198=60p
3. p=3.3
4. Subbing p=3.3 into either equation will give us:
5. Q_s=88+40(3.3)
6. Q_s=220

How market forces work when out of equilibrium.  The following scenarios begin with a price:

1. Above the equilibrium, leaves us with excess supply.  The firms can sell excess inventory by lowering the price, and this continues until the price is at equilibrium and Q_d=Q_s.
2. Below the equilibrium, leaves us with excess demand.  Some buyers are willing to pay more and will bid up the price and firms will increase price and supply more, this continues until equilibrium in the market is reached.

There are several types of shocks that will take us out of market equilibrium:

1. Shocks to supply: changes in input prices, technological change, anything that changes a determinant of supply (and is present in your explicit supply function)
2. Shocks to demand: changes in preferences, more consumers, a change in price of a related good, anything that changes a determinant of demand (and is present in your explicit demand function)
3. Shocks that affect both: expectations of future prices changing, or any other variable present in both functions.

Government intervention – Quotas and bans can change the supply function, either restricting the amount supplied, or possibly kinking the supply curve.

Government intervention – price controls

1. Price ceiling – for example, a rent control law
2. Price floor – for example, minimum wage law