16 May CALCULATE THE SUBSTITUTION EFFECT AND THE INCOME EFFECT.ILLUSTRATE IT ON A GRAPH.
Provide complete work that leads to each answer. Do the problems in the order given. Only hard copies are accepted. Staple your pages together.
Instructor: Ming Li
1. (10 points) TRUE or FALSE (Determine if each of the following statements is true or false. Explain your reasoning. All credits are assigned to explanations).
(a) Assume the prices of all goods are positive. The Engel curve of each good must pass through the origin.
(b) If a good is an inferior good, then the substitution effect and theincome effect are of opposite signs.
(c) If the consumer has Cobb-Douglas preferences, it is impossible forone of the goods to be a Giffen good.
(d) If a consumer has quasilinear preferences over two goods, then herconsumption of neither good depends on her level of income.
2. (10 points) Based on the following demand functions, determine whether good 1 is a normal good or inferior good, whether it is an ordinary good or Giffen good, and whether good 2 is a substitute or complement for good
1.
(consider only the combinations of prices
and incomes such that x1(p1,p2,m) ≤ m/p1, i.e., do your analysis ignoring the possibility that x1(p1,p2,m) > m/p1).
3. (10 points) Consider the utility function u(x,y) = 2lnx + lny. Initially, the prices are px = $2/unit and py = $1/unit. The consumer has an income of $24. Illustrate your answers with graphs.
(a) (2 points) Derive the consumer’s optimal consumption bundle.
(b) (2 points) Now suppose the price of good x increases to = $3/unit. What is the new optimal consumption bundle?
(c) (3 points) Calculate the substitution effect and the income effect.Illustrate it on a graph.
(d) (3 points) Calculate the compensating variation and equivalent variation of the price change.
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4. (10 points) Connie, as you may recall, always takes one cup of cookies with one cup of coffee. Cookies cost $2 per cup, and coffee costs $1 per cup. Connie has $12 to spend on cookies and coffee. Consider a price drop in cookies to $1 per cup.
(a) (4 points) Illustrate Connie’s optimal consumption bundles beforeand after the price change with a graph. Explain your reasoning.
(b) (6 points) Decompose the change in Connie’s consumption of cookiesinto the income effect and the substitution effect. Illustrate them in the graph.
5. (10 points) Suppose a consumer’s demand for good 1 is given by x1(p1,p2,m) = m/(2(p1 + p2), and she spends all her income on these two goods.
(a) (3 points) Find the consumer’s demand for good 2. (Hint: use thebudget equation.)
Now, let the initial prices be p1 = 2 and p2 = 2, and let m = 48. Suppose the price of good 1 drops to
(b) (3 points) Is good 1 a normal good or inferior good? Ordinary orGiffen? Is good 2 a complement or substitute for good 1?
(c) (2 points) Are the consumer’s preferences homothetic?
(d) (4 points) Calculate the change in the consumption of good 1 due tothe income effect and substitution effect. (Hint: read the example in the textbook.)
6. (10 points) A consumer’s demand for hockey memorabilia is x(p) = 100−p.
(a) (4 points) At price p = 40, what is the total benefit she derives from consuming hockey memorabilia? What is her consumer’s surplus?
(b) (6 points) Suppose now the price rises to p0 = 50, what is the change in her consumer’s surplus? What part of the change is due to increased cost of buying hockey memorabilia, and what part of the change is due to the reduced consumption of hockey memorabilia?
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