Lesson 1, Topic 1
In Progress

1.4. An example: Supply and demand in a 6 person economy (or new venture)

ryanrori December 23, 2020

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Supply and demand can be thought of in terms of individual people interacting at a market. Suppose the following six people participate in this simplified economy:

  • Alice is willing to pay R10 for a sack of potatoes.
  • Bob is willing to pay R20 for a sack of potatoes.
  • Cathy is willing to pay R30 for a sack of potatoes.
  • Emily is willing to sell a sack of potatoes for R15.
  • Fred is willing to sell a sack of potatoes for R25.

There are many possible trades that would be mutually agreeable to both people, but not all of them will happen. For example, Cathy and Fred would be interested in trading with each other for any price between R25 and R30. If the price is above R30, Cathy is not interested, since the price is too high. If the price is below R25, Fred is not interested since the price is too low. R25, so she will not trade with Fred at all. In an efficient market, each seller will get as high a price as possible, and each buyer will get as low a price as possible.

Imagine that Cathy and Fred are bartering over the price. Fred offers R25 for a sack of potatoes. Before Cathy can agree, Emily offers a sack of potatoes for R24. Fred is not willing to sell at R24, so he drops out. At this point, Dan offers to sell for R12. Emily won’t sell for that amount so it looks like the deal might go through. At this point Bob steps in and offers R14. Now we have two people willing to pay R14 for a sack of potatoes (Cathy and Bob), but only one person (Dan) willing to sell for R14. Cathy notices this, and doesn’t want to lose a good deal, so she offers Dan R16 for his potatoes. Now Emily also offers to sell for R16, so there are two buyers and two sellers at that price (note that they could have settled on any price between R15 and R20), and the bartering can stop. But what about Fred and Alice? Well, Fred and Alice are not willing to trade with each other since Alice is only willing to pay R10 and Fred will not sell for any amount under R25. Alice can’t outbid Cathy or Bob to purchase from Dan so Alice will not be able to get a trade with them. Fred can’t underbid Dan or Emily so he will not be able to get a trade with Cathy. In other words, a stable equilibrium has been reached.

A supply and demand graph could also be drawn from this. The demand would be:

  • 1 person is willing to pay R30 (Cathy).
  • 2 people are willing to pay R20 (Cathy and Bob).
  • 3 people are willing to pay R10 (Cathy, Bob, and Alice).

The supply would be:

  • 1 person is willing to sell for R5 (Dan).
  • 2 people are willing to sell for R15 (Dan and Emily).
  • 3 people are willing to sell for R25 (Dan, Emily, and Fred).

And here is the graph:

Supply and demand match when the quantity traded is two sacks and the price is between R15 and R20. Whether Dan sells to Cathy, and Emily to Bob, or the other way round, and what precisely is the price agreed cannot be determined. This is the only limitation of this simple model. When considering the full assumptions of perfect competition the price would be fully determined since there would be enough participants to determine the price. For example, if the “last trade” was between someone willing to sell at R15.50 and someone willing to pay R15.51, then the price could be determined to the cent. As more participants enter, the more likely there will be a close bracketing of the equilibrium price.

It is important to note that this example violates the assumption of perfect competition in that there are a limited number of market participants. However this simplification shows how the equilibrium price and quantity can be determined in an easily understood situation. The results are similar when unlimited market participants and the other assumptions of perfect competition are considered.

Larger quantities will be sold at lower prices and smaller quantities at higher prices. This relationship is called the LAW OF DEMAND.

Why will a higher price cause a decrease in the quantity demanded? The answer is that every product can be replaced by another product.

When the price of a certain product increases too much, the consumer will have to buy less of that product and more of a cheaper substitute that is equally good.

Assume that you and your two mates, Betty and Richard, played video games at the café yesterday. If each video game cost R5 per turn you would not be able to play often because it is too expensive.

Had the video games cost less, e.g. R1 per turn, you would be able to play more games.

The following table indicates the quantity of video games that you will be willing to play per day at various prices.

PRICE PER VIDEO GAMEYOUR AMOUNT DEMANDED PER DAYBETTY’S AMOUNT DEMANDED PER DAYRICHARD’S AMOUNT DEMANDED PER DAYTOTAL AMOUNT DEMANDED PER DAY
R1,00          8          5           8           21
R2,00          6          4           7           17
R3,00          4          3           5           12
R4,00          3          2           4           9
R5,00          1          0           1           2

Indicate, graphically, the total quantity of video games demanded per day at the different prices:

The graph indicates the relationship between the price of the video games and the quantity demanded per day. In total they are prepared to play 21 video games per day at a price of R1 per turn.

If the price per video game is R4.00 the demand for games per day will be less, only 9. This indicates the negative relationship between the demand for goods and the price of goods (the law of demand). An increase in price will lead to a decreased quantity demanded.

You ask your classmates how many videos they would be willing to hire per weekend at the following prices:

PRICE PERTOTAL QUANTITY
VIDEODEMANDED
R10,0050
R15,0040
R20,0030
R25,0020
R30,0010

a) Construct a total demand curve of your classmates for the hire of videos.

b) What is the total quantity that can be hired per weekend at R25,00?

c) How is the law of demand illustrated?

d) How much money is spent per weekend if the videos cost R15,00 each?

Supply

It is the quantity of a product that a producer or entrepreneur supplies for sale at a given point of time. Supply measures the quantity supplied (per day, week or year) at a given price. The quantity supplied by the producer or entrepreneur is determined by the relationship of the price to the cost of production or the cost price of the product.

The higher the selling price, the greater the quantity supplied by the entrepreneur to ensure maximum profit.