Question

1. Consider a pure exchange economy with 2 goods

(X and Y) and 2 consumers (A and B) having

utility functions

Consumer A u
A) yA, who is endowed with

(2, 6) of the commodities;

Consumer B u
BUB
who is endowed with

(4, 2) of the commodities.

Compute the market equilibrium price and

quantity combinations of the consumers that will

result in efficient allocation of resources.

Answer 1

Answer on Question # 76339, Economics -Microeconomics:

Question: Consider a pure exchange economy with 2 goods (X and Y) and 2 consumers (A and B) having utility functions Consumer A, $u_A = Y_A$, who is endowed with (2, 6) of the commodities; for Consumer B, $u_B = Y_B$ who is endowed with (4, 2) of the commodities.

Compute the market equilibrium price and quantity combinations of the consumers that will result in efficient allocation of resources.

Solution: Here, $X_0^A = 2$, $Y_0^A = 6$ and $X_0^B = 4$, $Y_0^B = 2$.

So, $X_0^A + X_0^B = 6$ and $Y_0^A + Y_0^B = 8$.

Now, market demand is given by,

$$X_A = 1 + 3P$$ $$Y_A = \frac{1}{P} + 3$$ $$X_B = 2 + P$$ $$Y_B = \frac{2}{P} + 1$$

Where, $P =$ price

So, market demand for X is given by,

$$X = 3 + 4P \quad \text{...(1)}$$

Similarly, market demand for Y is given by,

$$Y = 4 + \frac{3}{P} \quad \text{...(2)}$$

Market equilibrium condition for X is given by,

$$3 + 4P = 6$$ $$\text{or, } P = \frac{3}{4}$$

Similarly for Y is given by,

$$P = \frac{3}{4}$$

Answer: Market equilibrium price for X is $\frac{3}{4}$ and quantity for X is 6.

Market equilibrium price for X is $\frac{3}{4}$ and quantity for X is 8.

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