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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.

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Copyright (c) Christopher Makler / econgraphs.org