Sign Analysis of the Price Change Resulting from a Demand Shock (∂P*/∂a)

In a market model, after differentiating the equilibrium condition with respect to a demand parameter 'a', you arrive at the following equation:

(∂D/∂P) * (∂P*/∂a) + (∂D/∂a) = (∂S/∂P) * (∂P*/∂a)

Where P* is the equilibrium price, D is the demand function, and S is the supply function. Which of the following correctly isolates the partial derivative (∂P*/∂a) to show how the equilibrium price changes with respect to the parameter 'a'?

In a market analysis, after differentiating the equilibrium condition with respect to a demand parameter 'a', the following equation is obtained:

(∂D/∂P) * (∂P*/∂a) + (∂D/∂a) = (∂S/∂P) * (∂P*/∂a)

Arrange the subsequent algebraic steps into the correct logical sequence to isolate the term ∂P*/∂a, which represents the change in equilibrium price with respect to the parameter.

Isolating a Variable of Interest

Analyzing a Flawed Algebraic Derivation

Consider a standard market model where the equilibrium condition has been differentiated with respect to a demand parameter 'a', resulting in the equation:

(∂D/∂P) * (∂P*/∂a) + (∂D/∂a) = (∂S/∂P) * (∂P*/∂a)

where P* is the equilibrium price, D is the demand function, and S is the supply function.

True or False: The correct algebraic rearrangement to isolate the term representing the change in equilibrium price (∂P*/∂a) is:

∂P*/∂a = (∂D/∂a) / [ (∂D/∂P) - (∂S/∂P) ]

In a standard market model, the process of finding how a change in a demand parameter 'a' affects the equilibrium price (P*) begins with differentiating the equilibrium condition. This results in the following equation:

(∂D/∂P) * (∂P*/∂a) + (∂D/∂a) = (∂S/∂P) * (∂P*/∂a)

The next goal is to algebraically rearrange this equation to solve for ∂P*/∂a. Match each equation representing a step in this rearrangement with the algebraic principle that justifies it.

In a market analysis, the equation (∂D/∂P) * (∂P*/∂a) + (∂D/∂a) = (∂S/∂P) * (∂P*/∂a) is derived to understand how a parameter a affects the equilibrium price P*. The next algebraic step is to group terms and factor out ∂P*/∂a. Complete the following rearranged version of the equation by filling in the blank: (∂D/∂a) = [______] * (∂P*/∂a)

Rationale for Isolating the Equilibrium Price Derivative

In a market model, an economist is analyzing how a change in a supply-side parameter, 't' (such as a per-unit tax), affects the equilibrium price, P*. After differentiating the market equilibrium condition with respect to 't', the following equation is derived:

(∂D/∂P) * (∂P*/∂t) = (∂S/∂P) * (∂P*/∂t) + (∂S/∂t)

Where D is the demand function and S is the supply function. Which of the following correctly isolates the partial derivative (∂P*/∂t) by rearranging the equation?

Evaluating Algebraic Manipulations in Comparative Statics