• Simple algebra to find equilibrium prices and quantities if we know supply and demand functions

• Remember, supply and demand are each mathematical functions relating price to quantity:

  • Demand: $q_D=10-p$
  • Supply: $q_S=2p-8$

• We know at equilibrium: $q_D=q_S$

1. Find equilibrium quantity and price $(q^{\star },p^{\star })$.

2. Sketch a rough graph.

• Markets allocate resources based on individuals’ reservation prices:

  • Buyers’ max. willingness to pay
  • Sellers’ min. willingness to accept

• Goods flow to those who value them the highest and away from those who value them the lowest

• It might look like it, but competition in markets is NOT between buyers vs. sellers!

• In markets:

  • buyers compete with other buyers &
  • sellers compete with other sellers

• Buyers want to pay the lowest price to buy a good

• But they face competition from other buyers over the same scarce goods

• Buyers attempt to raise their bids above others' reservation prices to obtain the goods

• Sellers want to get the highest price for a good they sell

• But they face competition from other sellers over the same potential customers

• Sellers attempt to lower their asking prices below others' reservation prices to sell their goods

• Supply and demand set the market-clearing price for all units exchanged (bought and sold)

• Demand function measures how much you would hypothetically be willing to pay for various quantities

  • "reservation price"

• You often actually pay (the market-clearing price, $p^{\ast })$ a lot less than your reservation price

• The difference is consumer surplus

$$CS=WTP-p^{\ast }$$

$$\begin{array}{cc}CS& =\frac{1}{2}bh\\ CS& =\frac{1}{2}(5-0)(\$10-\$5)\\ CS& =\$12.50\end{array}$$

• An increase in market price reduces consumer surplus

$$\begin{array}{cc}C{S}^{\prime }& =\frac{1}{2}bh\\ C{S}^{\prime }& =\frac{1}{2}(3-0)(\$10-\$7)\\ C{S}^{\prime }& =\$4.50\end{array}$$

• An decrease in market price increases consumer surplus

$$\begin{array}{cc}C{S}^{\prime }& =\frac{1}{2}bh\\ C{S}^{\prime }& =\frac{1}{2}(7-0)(\$10-\$3)\\ C{S}^{\prime }& =\$24.50\end{array}$$

• Supply function measures how much you would hypothetically be willing to accept to sell various quantities

  • "reservation price"

• You often actually receive (the market-clearing price, $p^{\ast })$ a lot more than your reservation price

• The difference is producer surplus

$$PS=p^{\ast }-WTA$$

$$\begin{array}{cc}PS& =\frac{1}{2}bh\\ PS& =\frac{1}{2}(5-0)(\$5-\$0)\\ PS& =\$12.50\end{array}$$

• An increase in market price increases producer surplus

$$\begin{array}{cc}P{S}^{\prime }& =\frac{1}{2}bh\\ P{S}^{\prime }& =\frac{1}{2}(7-0)(\$7-\$0)\\ P{S}^{\prime }& =\$24.50\end{array}$$

• An decrease in market price decreases producer surplus

$$\begin{array}{cc}P{S}^{\prime }& =\frac{1}{2}bh\\ P{S}^{\prime }& =\frac{1}{2}(3-0)(\$3-\$0)\\ P{S}^{\prime }& =\$4.50\end{array}$$

• A good visual rule of thumb:

• Compare distance between choke price and $p^{\ast }$ for each curve

• Bigger distance $⟹$ less elastic in equilibrium (and vice versa)

  • $⟹$ more surplus