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Chapter 17 / The Circular Flow and General Equilibrium

17.2 Conditions for General Equilibrium

In Unit I, Chuck’s optimal bundle was the point along the PPF where his MRS was equal to his MRT:

In Chapter 16, we solved for the equilibrium economy-wide quantities as functions of the prices of all goods: that is, $Y_1^\star(p_1,p_2)$ and $Y_2^\star(p_1,p_2)$. We found that economy would choose the point along the PPF where the MRS was equal to the price ratio, $p_1/p_2$, as shown in the left-hand graph below. In this chapter, we’ll give the resulting income to consumers and find their optimal quantity of goods to consume, $X_1^\star(p_1,p_2)$ and $X_2^\star(p_1,p_2)$, as shown in the right-hand graph:

We will then find the prices which result in all markets clearing: that is, where $X_1^\star(p_1,p_2) = Y_1^\star(p_1,p_2)$ and $X_2^\star(p_1,p_2) = Y_2^\star(p_1,p_2)$.

We will proceed in steps:

  1. Firm profit maximization. Find output as a function of prices: \(Y_1^\star(p_1,p_2)\) \(Y_2^\star(p_1,p_2)\)From that output, determine GDP: \(M(p_1,p_2) = p_1Y_1^\star(p_1,p_2) + p_2Y_2^\star(p_1,p_2)\)
  2. Consumer utility maximization. Find the consumer’s optimal quantities of goods 1 and 2, facing prices $p_1$ and $p_2$ and having $M(p_1,p_2)$ from step 1 as their income: \(X_1^\star(p_1,p_2) = x_1^\star(p_1,p_2,M(p_1,p_2))\) \(X_2^\star(p_1,p_2) = x_2^\star(p_1,p_2,M(p_1,p_2))\)
  3. Market clearing. Set demand equal to supply: \(X_1^\star(p_1,p_2) = Y_1^\star(p_1,p_2)\) \(X_2^\star(p_1,p_2) = Y_2^\star(p_1,p_2)\) and solve for the equilibrium prices of goods 1 and 2.

What we’ll find is that when the system is in equilibrium, we will have found the point along the PPF where $MRS = MRT$: that is, the exact same point Chuck would have chosen if he were just maximizing utility subject to his PPF.

Previous: The Circular Flow
Next: Step 1: Firm Optimization
Copyright (c) Christopher Makler /