uppose a consumer has preferences between two goods that are perfect substitutes. In this case would the consumers be better off or worse off if the tax with rebate based on original consumption were in effect?
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- Consider the following Marshallian Demand Function derived from the utility maximization problem, X = a M P where X is the quantity consumed, Mis income of the consumer, P is the price of the good, and α is some number between 0 and 1 which represents the relative importance of the good. Does this demand function satisfy the law of demand? (_ Why or why not? (*Suppose two goods, X and Y, are perfect complements and U = MIN (X, Y). A consumer has $24 to spend. Initially, the price of each good is $2. If the price of good X falls to $1, how much of the total change in quantity demanded of good X is due to the income effect? (Hint: Sketch the graph.)Two students, Nick and Sofia, are discussing normal and inferior goods. Nick says that if Frodo buys more beer when the price of beer goes up, then beer must be an inferior good for Frodo. If, on the other hand, he buys less beer when the price of beer goes up, then beer must be a normal good for Frodo. Sofia disagrees: "Normal and inferior goods are about income changes, not price changes. Therefore, we do not have enough information: beer could be an inferior or normal good in either of these cases." Do you agree or disagree? Carefully explain your point of view. Support your argument with graphs of income, substitution and total effects (please put beer on the horizontal axis and the other goods on the vertical axis). Please assume that Frodo's preferences over beer and other goods are strictly convex and satisfy "more is better" assumption.
- QUESTION 12 The consumer's utility function is the following: U=x+4x09 1 2 X = The consumer's optimal values of x and x2 are the given by the following: x1 I P 3.6P 1 3.6P 1 2 1 1-0.9 1 1-0.9 P 1 P P P 2 2 3.6P 0.9 3.6P 1 1 1 The compensated demand equations for x, and x, are the following: x = U-4 1-0.9 1-0.9 = 1 2 lc P 2c P 2 2 Assume the prices are the following: P=4, P=6, I=100000, and the P, that makes x =0 is P=4.422. 1 2 1 1 What is the consumer surplus?Which of the following is true of a Giffen good? It is a particular case of an inferior good where the income effect is greater than the substitution effect and runs counter to it. It is similar to an inferior good, though the income effect is positive and more significant than the substitution effect. It is similar to an inferior good, though the income effect is not as significant for the Giffen good as it is for the inferior good. It is most prevalent in developing economies.Economics Consider a household whose preferences are described by the utility function U(X1, X2) = X1X2 where X1 and X2 are household’s consumption of goods 1 and 2 respectively. Consider that household’s budget constraint is: P1X1 +P2X2 =I. (a) Derive the household’s demand functions for goods X1 and X2. (b) Derive the household’s compensated demand function for goods 1 and 2, i.e., obtain functions of the form Xi = fi (P1, P2, U) , I = 1, 2 where U is the household’s level of utility. (c) Assume that in the initial situation the commodity prices, P1 and P2, and the household income level, I, are given by P1 = $1, P2 = $1 and I = $2. Sketch the compensated and uncompensated demand curves for good 2 with P1 held constant at the initial level. In the compensated case, U is held constant at the initial level while in the uncompensated case, I is held constant. (d) By how much must I be increased if P2 increases to $2 (P1 remains at $1) and our household is to maintain its…
- Suppose that the marginal utilities from consuming good X and good Y are MU, -15 and MUy = 20. The price of good X and good Y are Px = $2 and $3 respectively. Which of the following statements is true? The consumer receives more marginal utility per dollar from good Y than from good X The consumer could increase utility by giving up 1 unit of good X for 2/3 units of good Y The consumer could increase utility by giving up 1 unit of good Y for 3/2 units of good X Jy The consumer is maximizing utilitySuppose that after your income increases, you consume less fast food. This means: Fast food is considered an inferior good. Coke and Pepsi are substitutes. Coke and fried chicken are complements. None of the above.True/False? Briefly explain. Assume good x is a normal good. In terms of consumer behavior, a cash grant and a small (relative to the initial consumption of x) limited non-matching grant on good x (with the limit that is equal to the cash grant) are essentially equivalent.
- Lan's utility function is U = xa y1-a where x denotes her consumption of good X, y denotes her consumption of good Y and a = 0.8. The price of good X is Px = 7, the price of good Y is Py = 14 and Lan's income is M = 338. If each price increases by 2 dollars, how much money must Lan be given to compensate her for the price increase?For a consumer with a utility function u=3x^2y^2 when px=3 and py=4, find the consumption levels that maximize his utility under the $120 budget constraint. What is the maximum benefit?Assume a consumer has a utility function given by u(x,y)=x+y , with an income of $100. Consider a $1 per-unit tax on good 1. Suppose a lump sum tax raises the same amount of income as the per-unit tax. How much income must it raise?