A consumer must division $250 between the consumption of product x and product y. The relevant market prices are px=$5 and py=$10.
1. Determine the market rate of substitution
2. Write the equation for the consumer's budget line
3. Illustrate the consumer's opportunity set in a carefully labeled diagram
4. Show how the consumer's opportunity set changes when the price of good x increases to $10.
5. How does this change alter the market rate of substitution between goods x and y?
Give a rationale to your answer
1. The market rate of substitution is the ratio of the prices of the two goods. In this case, it is given as px/py = 5/10 = 0.5.
2. The equation for the consumer's budget line can be written as:
5x + 10y = 250, where x is the quantity of product x consumed and y is the quantity of product y consumed.
3. The consumer's opportunity set can be illustrated in a diagram with product x on the x-axis and product y on the y-axis. The budget line will be a straight line with intercepts at x=50 and y=25.
4. When the price of good x increases to $10, the new budget line equation becomes:
10x + 10y = 250. The intercepts of this line are x=25 and y=25. So, the opportunity set is now constrained along the x-axis, with the consumer only able to afford up to 25 units of product x.
5. This change alters the market rate of substitution between goods x and y because the consumer can now purchase fewer units of good x for the same amount of money. This means that the consumer will have to give up more units of good y to increase consumption of good x by one unit, leading to a higher rate of substitution.