Suppose is preferences are represented by the following utility function: u=x-y. Which of the following statements is true? m i's Marshallian demand for good y is y=- m i's Marshallian demand for good x is x=- O i will consume more good y than good x i will consume the same amounts of good x and good y
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- Recent research confirms that the demand for cigarettes is not only inelastic, but it also indicates that smokers with incomes in the lower half of all incomes respond to a given price increase by reducing their purchases by amounts that are more than four times as large as the purchase reductions made by smokers in the upper half of all incomes. How can the income and substitution effects of a price change help explain this finding?Darwin consumes cigarettes (x1) and other goods (x2). His preferences are given by UD(q1,q2)=4lnq1 +q2The quantity of good 2 is measured in units of income and so you can assume that throughout this problem, the price of good 2 is normalized p2 = 1 (a) Using the Lagrangian, derive Darwin’s uncompensated demand for cigarettes: D1D(p1,Y). Note that we are holding p2 =1 and so that is not a variable in the demand function. Using the Lagrangian, derive the equation λ∗(p1, Y ). Provide an economic interpretation of the Lagrange multiplier. Does it vary with income, Y ?1. John consumes good X and good Y. His expenditure function is E=2U(PX)^5(PY)^5. His demand for goods X and Y are given by X=I/(2 PX), Y= I/(2 PY) Suppose that initial PX=1 and PY=1. John's income is 12. a. Find John's initial level of utility. b. Suppose the government announces plans to introduce a tax of 3 per unit on good X. Find an exact expression for the amount of income John would be just willing to give up to avoid the tax on good X. c. Suppose the government implements the tax. How does John's consumption of good X change? Find the income and substitution effects (with regards to good X) associated with the tax increase.
- Consider the consumer's problem with two goods, good X and good Y. Is it possible that the budget line of the consumer, given by the equation pyX + PyY = I shifts to the right and parallel to its original position in (X, Y) plane while the income () remains constant? Provide an analytical explanation for your response. (Hint: the budget line shifts to the right and parallel to its original position when the income I rises and prices constant. This question asks if the prices can change in a certain way that the budget line shifis as if income had increased.)In the bread market, Maria buys different amounts of bread conditional on whether the price is $2, $5, or $7 a loaf. To generate Maria’s demand curve for bread, what other set of information do we need? Group of answer choices: whether her bread consumption goes up or down with price how much bread she buys in total how much bread she buys at each price point whether or not she switches to a substitute when the price is highThe utility function of a consumer is u = √x + 2y. (a) Show mathematically that the rise of Px will decrease demand for x goods. (b) Demonstrate mathematically that an increase in Px will increase demand for goods y. (c) If currently the price of goods is four times more expensive than the price of goods x and the government wants to set a tax that results in the increase in Px′ = 1.1Px, what are the units of decrease in the number of x items requested?
- Draw the following scenario: Assume a piece of jewelry and 2 consecutive drops in its price. Also consider Alia’s demand to be relative elastic in the price range from ? 1to ? 2, and that she perceives jewelry as a Giffen good in the price range from ? 2to ? 4. Draw her price-consumption curve with well-behaved preferences. Clearly label your graph. The graph may be something like this:A consumer is in equilibrium when Px = 7 and Py = 4, and he is consuming 40 units of good X and 80 units of good Y. If Py increases to Rs. 5, he moves to a new equilibrium where he consumes 50 units of good X. Beginning from the new equilibrium, if income increases by Rs 100 and the consumer decides to consume 65 units of good Y, what will be the shape of the ICC and the Engel curve? Calculate and explain. Also draw the demand curve for Y indicating the above scenario.A consumer has preferences over two goods, denominated by x and y, given by the utility function U(x,y) = min{αx,y} with α > 0. The prices of the good are px = 2 and py = 5. The consumer has an income of I > 0. (a) Provide an intuition for this utility function. Specifically, are these goods substitutes or complements? If x is bicycle tires and y is bicycle frames, what is the value for α? (b) For what values of α will the consumer demand (i.e., Walrasian demand) more x than y. (c) For what values of α will the consumer spend more on x than on y (given her Walrasian demands).
- a. Determine the demand functions of x and y in the case of a Cobb-Douglas type utility function, in the following cases: α=0.40;β=0.60 Graph the demand functions of the two goods (price as a function of quantity) assuming the individual's income is $500 - Determine what is the quantity demanded of x and y, if the price of good x is USD 1, the price of good y is USD 4, and income is USD 500 - Now, explain what happens to the quantity demanded if the prices of the goods are doubles holding income constant.The demand for a good is QA=200+0.3I-PA+2PB, where QA is the quantity demanded of Good A, I is the individual’s income, PA is the price of Good A, and PB is the price of Good B. Which of the following statements is true? a. Good A is a normal Good. In addition, Goods A & B are substitutes. b. Good A is a normal Good. In addition, Goods A & B are complements. c. Good A is an inferior Good. In addition, Goods A & B are substitutes. d. Good A is an inferior Good. In addition, Goods A & B are complements.