4. (10 points) Graphically derive the Engel curve for a normal good assuming the consumer has...
Derive Roger's Engel curve Derive Roger's Engel curve for B. Recall that Roger's utility function is Cobb-Douglas, U = 30.75 0.25 his income is Y, the price of B is PB, and the price of Z is pz Roger's Engel curve for Bis Y = (Round any numerical coefficient to one decimal place and properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the character.)
Derive Roger's Engel curve for B. Recall that Roger's utility function is Cobb-Douglas, U=B0.20 20.80 his income is Y, the price of B is PB, and the price of Z is pz. Roger's Engel curve for B is Y= . (Round any numerical coefficient to one decimal place and properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the character.)
Imagine a representative consumer, whose utility for apples (X) and all other goods (Y) can be represented in a Cobb-Douglas form. 1) Please graphically represent consumer indifference curves, given prices Px and Py and the budget constraint M. 2) What will happen to consumer utility and optimal bundle if consumer income (budget) increases and apples are a necessity good? Please show graphically and explain the intuition. 3) How would the Engel curve look like for point #2?
A consumer gets utility from consuming commodities x1 and x2. The consumer's the Engel curve for x1 has a positive slope. True or False: It is not possible to determine the slope of the Engel curve for x2.
Problem 2 (30 marks) A consumer has a utility function (11,12)= = = (a) Express the consumer's demand for good l as a function of prices and income. (b) Draw an Engel curve for the consumer's demand for good 1 when the prices are given by Pi = 1, and P2 = 1. (c) Draw another Engel curve for the consumer's demand for good 1 when the prices are given by Pi = 1, and p2 = 3. (d) Draw...
2. Suppose there are two consumers in a country: consumer 1 and consumer 2. The two consumers have the following Cobb-Douglas utility function defined over consumption of goods X and Y: where 0 < β < 1. Each consumer has a different income, consumer 1 has income 1, while consumer 2 has income 12. For now, we will treat the income of each consumer as given. Denote aggregate income as I 12. (a) (10 points) Derive each consumer's individual Marshallian...
Exercise 5: Generating an individual demand curve Suppose that a consumer is only able to purchase two goods, ham and cheese. The consumer has an income of $6000. When Pham = $100 and Pcheese = $100, the consumer demands 15 units of ham and 15 units of cheese. When Pham = $50 and Pcheese = $100, the consumer demands 24 units of ham and 18 units of cheese. 1. Plot a budget line for each of the two pricing regimes....
Consider a consumer with income M who can buy two products, good 1 and good 2 for prices p1 and p2. If the consumer has Cobb-Douglas utility, show that her preferences are homothetic.
A consumer buys two goods, good X and a composite good Y. The utility function is given as ?(?,?) = ? + ?√? . 1) Derive the demand function for good X.(5 marks) 2) Is good X a normal or an inferior good? Why? ( 5 marks) 3) Suppose that initially ?? = $1 and then it falls and becomes ?? = $0.5. Also suppose that Income=$10. Calculate the substitution effect, income effect, and the price effect and show...
1. When a consumer has a Cobb-Douglas utility function given by u(x, y) = xa yb , their demand for good x is given by x∗ = m/Px (a/a+b) where m is income and Px is the price of good x. Using this demand function, find the formula for this consumer’s price elasticity of demand. Interpret it in words.