The demand for each of the factors of production is often referred to as a "derived" demand to emphasize the fact that the relationship between the factor's price and the quantity of the factor demanded by firms employing it in production is directly dependent on consumer demand for the final product(s) the factor is used to produce. If for some reason (say, for example, a spontaneous shift in consumer tastes) the demand for men's hats increases (shifts to the right) so that more hats than before can be sold at any given price, then the "derived" demand for felt used in making hats will also increase (shift to the right) so that felt-makers will be able to sell more felt at any given price. (We would also expect the hat-makers' demand for the labor of hatters and for specialized hat-making machinery to shift to the right in a similar fashion in response to the public's greater demand for hats.)
What is the mechanism by which a shift in demand for the final product is translated into a shift in demand for the factors of production used in its manufacture? The key is the change in the price of the final product brought about by the shift in demand for it. If the demand curve for hats shifts to the right and the (upwardly sloping) supply curve remains unchanged, then the equilibrium price and quantity in the hat market will now involve both a somewhat higher price for hats and a somewhat larger quantity of hats being produced and sold to the public. (Because of the price rise, the marginal revenues earned by the manufacturers per additional hat sold will be higher, so consequently their desire to maximize profits will lead them to produce additional hats until the marginal cost for the last hat rises to equal the new higher price.) But producing more hats than before will require more of the relevant factors of production than before, which they will want to purchase from their suppliers, shifting the demand curves for each of the factors to the right. (This increase in demand for the factors in turn will tend to raise the factor prices somewhat and to increase the quantity of them sold, which then affects the factor producers' demand for their own necessary inputs and brings about further price-and-quantity adjustments throughout the economy in an ever-widening ripple effect.)
[See also: factors of production demand demand, law of demand curve demand schedule supply supply, law of supply curve supply schedule marginal analysis ]