Why the diminishing marginal utility curve has the same slope as the demand curve

Diminishing marginal utility states that, the marginal utility of a product diminishes with each unit of the product consumed.

This is because, the change in utility, when each unit of product is consumed, always decreases. ( refer to a standard text for more clarity)

ILLUSTRATION

Fig 1

Consider an example of ordering pizza, which costs one dollar a slice. If consuming the first slice gives 24 utils of utility, after eating the next one, the total utils increases to 36 utils. Refer to fig 1 for the complete pizza consumption.

You may notice that, had the price of a slice of pizza been $2, then the utility also reduces by half for each slice.

Fig 2

If we draw the total utility against number of slices consumed, the plot will look like fig 2

And therefore, if you plot the marginal utility in y axis and the number of unit consumed, in the x axis, you always get a curve with diminishing curve. This is called the diminishing marginal utility curve as illustrated in the fig 3 below.

Fig 3

If marginal utility of a product  is Mx at a price x, then Mx/x ie the marginal utility per dollar for that product should always be greater than that of any other alternative product, so that you may keep buying it.

So some one has to make you buy the same product  again and again, over every other alternative products, then the ratio Mx/x needs to be made constant, every time you consume the product.

Since marginal utility keeps on decreasing, while we consume the same product again and again, Mx decreases when more quantity is bought.

So inorder to keep Mx/x constant, the only way to do is the decrease the price, in the same ratio of decrease in Mx.

So the greater the price reduction, the more you will consume or demand. This is why the demand curve has the same slope as the marginal utility curve.

The demand curve is a plot produced, when the demand ( measured in quantity ) is plotted in x axis and the price plotted in the y axis.

The demand curve also has negative slope, ie the demand always diminishes when price is increased, keeping all other factors constant.

In the above pizza example, the demand curve would look like this

ILLUSTRATION

Product 1

let the marginal utility for a product be 100, 80, 60, 40, 20 for the first 5 pieces, and the price for the fifth piece is 20, then Mx/x for fifth piece is 1.

Product 2

If the marginal utility for another product be 100, 90, 70, 50, 40, and the price of the fifth piece is 20, then Mx/x for the fifth piece is 2.

If the seller has to make you take the fifth piece of the first product over that of the second product, then the marginal utility per dollar of the first product should be more than 2 ( marginal utility per dollar of the second product) . Ie the price of the fifth piece of the first product has to be reduced below 10 in order to make you buy the fifth piece of the first product over that of the second product.

This means that whenever you increase a price of a product, the demand diminishes.