Question

A consumer is in equilibrium at point A in the accompanying figure. The price of good X is $5. 

a) What is the price of good Y? 

b) What is the consumer’s income? 

c) At point A, how many units of good X does the consumer purchase? 

d) Suppose the budget line changes so that the consumer achieves a new equilibrium at point B. What change in the economic environment led to this new equilibrium? Is the consumer better off or worse off as a result of the price change?

The Graph needed for the question is provided

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Answer 1

a)

The maximum quantity of a commodity (good X) that is affordable with the given income (M) is:

The price of good X, and the maximum affordable quantity of good X is 20 units. Substituting the values in the relationship gives:

With income of $100 the maximum affordable quantity of good Y is 20 units. Hence the price of good Y is:

Therefore the price of good Y is

b)

The maximum quantity of a commodity (good X) that is affordable with the given income (M) is:

The price of good X, and the maximum affordable quantity of good X is 20 units. Substituting the values in the relationship gives:

Hence the consumer’s income is

c)

At the initial equilibrium point A, the consumer consumes 10 units of good Y at $5 each. Hence the money income spent in consuming good Y is $50.

The remaining $50 are used in consuming good X which is priced at $5 per unit. Therefore the consumer consumes 10 units of good X ($50/$5).

d)

At point B, the consumer is able to consume a more than twice the units of good Y. Note that the maximum affordable quantity of good X is still 20 units while the maximum affordable quantity of good Y has increased to 40 units. This implies that the the price of good Y has fallen which has enabled the consumer to consume more units of relatively inexpensive good Y.

To analyze if the consumer is better off or worse off, first compute the reduction in the quantity consumed of good X. Since the consumer can consumes 40 units of good Y as the maximum affordable quantity with unchanged income of $100, the price of good Y has fallen to:

This implies that consumer spent $62.50 on the purchase of good Y (25 units at $2.50 per unit), remaining $37.50 are used in consuming good X which is still priced at $5 per unit. Therefore the consumer consumes 7.5 units of good X ($37.50/$5).

Since the reduction in the quantity of good X is smaller than the increase in the quantity of good Y, it can be concluded that the consumer is better off as more is always preferred to less.