Dear Reader,

It has come to my attention that Trump has decided that the USA will impose a 20 % tax on all goods from Mexico. Now before we get going I am not going to enter a debate today on the moral issues, I will simply consider the effect on the market of goods in the USA and Mexico.

Now many of you have heard of supply and demand curves, this is often misunderstood there is no “supply and demand” curve. Instead there are two curves, a supply curve and a demand curve.

Now if we consider the supply first, you should understand that the higher a price is then the more people are willing to sell a product. As a result the higher the price of the item the greater the supply of the item to the market will be.

We can express this as

Amount for sale at price **x** = S + K’**x**

We can consider the buying of a product, now in a simple world the cheaper the price then then more people who are willing to buy the product. We can express this as

Amount which will be consumed at price **x** = C – (Kx)

If we combine the two equations then we can get the equilibrium price for an item.

First

A = S + k’x

A= C – kx

Subtract one equation from the other to give us

0 = (S-C) + [x(k’+ k)]

C-S = k’x + kx

(C-S)/x = k’ + k

1/x = (k’+ k)/(C-S)

x = (C-S)/(k’+ k)

This allows us to get the point at which the two lines cross, this allows us to work out the price of the product.

If we take some made up values then we get the following graph. Amount is on the y axis and price on the x axis.

The values I used were k = 1, k’ = 1, S = 0.2 and C = 3.2 which gives us a value according to my equation of 1.5 for the price. Either the supply or demand equation will give us the same answer of 1.7 units per time period.

Now we have done the simple case we will try a little harder and consider adding tax to the system.Lets start with a fixed amount of tax per item such as a fixed tax in pence per bottle of beer.

Now an ugly way of doing it is to write.

C-S = (k’x) + [k(x+T)]

This will make a mess as it makes it harder to find x from the five constants. A better way is to calculate a new value of C from the value of T and K. In this simple model the equation for consumption is

A = C – kx

Now we can add the tax effect

A = C – (kx + kT)

We can rearrange this to give us

A = (C-kT) – kx

Now we can start again with our equation writing

A = S + k’x

A = (C- kT) – kx

0 = S – (C – kT) + (k’x + kx)

0 = [(S + kT) – C] + (k’x + kx)

-[(S + kT) – C] = (k’x + kx)

C – (S + kT) = (k’x + kx)

[C – (S + kT)]/x = k’ + k

1/x = (k’ + k)/[C – (S + kT)]

x = [C – (S + kT)]/(k’ + k)

If we keep T at a constant value we will get a new demand curve, here in the following graph I have shown the extra line. What we now see is that the we have a new curve, this shows that the consumption of the product is now lower. With a tax (T) of 0.3 the price which the seller sees will be 1.35 while the buyer sees a price of 1.65.

Also consumption will have been reduced from 1.7 to 1.55 per unit time. Now we are selling less both the producer and the seller are having not such a good time as they used to have.

Now we can make a graph of the amount of a produce which sells as a function of the tax and also the amount of tax money that the goverment make. You should see very quickly that tax can serve two purposes, it can serve the purpose of making money for the goverment and it can also be used to discourage the purchase of an item. It is important to note that the amount of tax required to make the most money is smaller than the amount required to do a better job of discouraging consumption. I have included in these graphs areas of negative tax to show what happens if the goverment use a subsidy to encourage spending on an item.

Now here is the same data with the tax expressed as the percentage of the net price.

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