Chapter 3: Comparative Statics & Demand
Short Answer Questions
1. Graphically compare the positions of the budget constraint when the price of good Y increases and decreases respectively, assuming the price of good X and income remain unchanged.
Answer:
Start from the first budget constraint (BL1). An increase in the price of good Y changes the position of the budget constraint from BL1 to BL2. In contrast, an increase in the price of good Y changes the position of the budget constraint from BL1 to BL3.
2. Show how to graphically derive the price consumption curve for good Y which is a normal good.
Answer:
3. What is the different between the price-consumption curve and the income –consumption curve?
Answer:
The price consumption curve shows the set of consumption bundles traced out as the price of a commodity varies, ceteris paribus. The income consumption curves shows the set of consumption bundles traced out as the level of income varies, ceteris paribus.
4. Explain and graphically show how an increase in income affects the demand curve when the good is normal?
Answer:
Since the good is normal, an increase in income increases the consumption at each price level. As a result, the demand curve shifts outwards.
5. “The income-consumption curve is also known as the Engel curve.” Is this statement true or false? Explain your answer.
Answer:
False. The income consumption curves shows the set of consumption bundles traced out as the level of income varies, ceteris paribus. We use this curve to derive the Engel curve which shows the relationship between the quantity demanded for a commodity and income, holding all pieces constant.
6. Good Y is a complement for good X. Graphically show the effect of a decrease in price of good Y on the demand curve of good X.
Answer:
7. If good X is inferior and good Y is normal, graphically show the effect of an increase in income on the quantities demanded for both goods when prices are unchanged.
Answer:
8. If both goods, X and Y, are normal, graphically show the effect of a decrease in income on the quantities demanded for both goods when prices are unchanged.
Answer:
9. Define what it is meant by “income elasticity of demand” and explain why the income elasticity of demand for a luxury good is greater than 1.
Answer:
The income elasticity of demand is defined as the percentage change in quantity demanded with respect to the percentage change in income. The quantity demanded for a luxury good is very responsive to changes in income. That is, one percentage increase in income leads to a greater percentage increase in consumption. As a result, its income elasticity is greater than 1.
10. Why the price elasticity of demand may be greater in the long run than in the short run? Explain.
Answer:
In the real world, it may take quite a while for a consumer to adjust their behaviour and fully respond to changes in price. Hence, one may expect the price elasticity to increase in the long run.
Essay Questions
1. Mr. A’s utility function is . Suppose that the prices of goods x and y are 2 and 1 respectively and his income is 10. What is his budget constraint? Find the demand function for each good. Explain your answer and comment how a change in price affects the demand for each good.
Brief answer:
The budget constraint is .
To find the demand function for each good, we first set the Lagrangean equation:
Using the first order conditions to solve for x and y, we will have the demand function of each good:
Each function shows how the quantity of each good varies with its price. As px (py) rises (falls), the demand for x (y) decreases (increases). In short, the relationship between price and demand is negative for both goods.
2. Mr. A’s utility function is . Suppose that the prices of goods x and y are 2 and 1 respectively and his income is 10. What is his budget constraint? Find the utility- maximising consumption bundle. Explain your answer.
Brief answer:
The budget constraint is .
To find the utility- maximising consumption bundle, we first set the Lagrangean equation:
Using the first order conditions to solve for x and y, the utility- maximising consumption bundle is .
3. Mr. B’s utility function is. Suppose the price of x is 2 and the price of y is 3 and his income is 12. What is his budget constraint? Suppose now the price of y decreases to 2. What is the new budget constraint? Explain and comment how such a change affects the position of the budget line and the utility- maximising consumption bundle.
Brief answer:
The budget constraint is which is drawn below (B1). Suppose now the price of y decreases to 2. The new budget constraint is which is drawn below (B2). Hence, an increase in the price of y rotates the budget line from B1 to B2.
From the graph, given the fist budget constraint, the utility- maximising consumption bundle is which yields a highest level of utility compared to other feasible bundles. An increase in the price of y moves the budget line from B1 to B2 and hence affects the utility - maximising consumption bundle which, as shown in the graph, now becomes .
4. “The slope of the Engel curve is always positive.” Is this statement correct? Explain your answer.
Brief answer:
This statement is not correct. For example, if good X is inferior, then the Engel curve showing the relationship between quantity demanded and income level have a negative slope. To explain, the reader should define the Engel Curve and may also show how to derive the Engel curve for good X which is income inferior.
5. Mr. C’s utility function is. What is the shape of Mr. C’s indifference curves? Comment on the characteristic of both goods. Explain what would happen to the demand curve for good x if the price of good y increases?
Brief answer:
The shape of Mr. C’s indifference curves is L-shaped as shown below.
As both goods are valuable when they are consumed together in a fixed proportion, they are complements. An example is a consumption of left and right shoes.
If the price of good y increases, the demand curve for good x shifts inwards.