Final answer:
To calculate dp/dy and dp/dw, we must totally differentiate the equilibrium condition Qd = Qs considering the demand and supply functions and their respective partial derivatives with respect to price, income, and wage rate.
Step-by-step explanation:
To find dp/dy and dp/dw by totally differentiating the equilibrium condition where quantity demanded (Qd) equals quantity supplied (Qs), we have to take into account the given functions Qd = D(p,Y) with Dp < 0, Dy > 0, and Qs = S(p, w) with Sp > 0, Sw < 0.
Here, p stands for the price of the commodity, Y is an exogenous income, and w is the exogenous wage rate. In equilibrium, we set Qd = Qs and totally differentiate with respect to Y and w to obtain the partial derivatives of the price with regards to income and wage rate, respectively.
In practical terms, suppose we have a demand equation Qd = 16 - 2P and supply equation Qs = 2 + 5P, equating them gives us an equilibrium condition.
This can be solved algebraically or graphed to find the equilibrium price and quantity. The solution indicates that if the price is $2 each, producers will supply 12 units of the commodity, confirming the correct equilibrium point found by both methods.