Assume that x1, x2 are ordinary goods. X₁ is an inferior good and x2 is a normal good. Draw a diagram of Slutsky decomposition of a price decrease. The rotation/shifts of the budget line • The optimal bundle before the price change (A) • The optimal bundle after accounting for only the substitution effect (B) • The optimal bundle after accounting for also the ordinary income effect (C), • The optimal bundle after accounting for the endowment income effect (D) Skip the indifference curves.
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- 2. Consider the following utility function: U(Qc,Qr) = Qc - QF Derive the relative demand for two goods as a function of endowments (Ec, Er) and relative prices pe/pPF-1 . Assume the budget constraint and the indifference curves are both linear. Assume the consumer is willing to tradeoff 1 of good X for 1 of good Y. If the relative price of one additional good X is giving up 1/2 of good Y, then the optimal bundle of the two goods is? Assume the budget constraint and the indifference curves are both linear. Assume the consumer is willing to tradeoff 1 of good X for 1 of good Y. If the relative price of one additional good X is giving up 1/2 of good Y, then the optimal bundle of the two goods is? Assume the government imposes an effective minimum wage (i.e., one above the equilibrium wage rate that would otherwise prevail in that market). Our supply and demand analysis implies? If preferences for pizza increase and the price of labor to produce pizza decreases, the equilibrium quantity of pizza will ____ and the equilibrium price of pizza will _____ .? Assume an intertemporal budget constraint that shows how consumption can be traded off between…Arya only consumes two goods: X and Y. When the price of X changes, the income effect and the substitution effect for X move in opposite directions. In addition, the income effect for X dominates the substitution effect. X must be: a) a Giffen good for Arya. b) an inferior good for Arya. c) a normal good for Arya. O d) perfect substitutes for Arya. O e) Both a and b are true.
- bundle on the boundary OI the Irasian buuget set? Explain. 3. Consider the utility function given by u (x1, x2) x1x3, and budget constraint given by P1x1 + P2x2 = w. (a) Find the optimal consumption bundle. (b) Find the wealth effect for each good. Is each good normal or inferior? (c) Graph the Engel curve for good 1. (d) Derive the wealth expansion path. (e) Derive the offer curve for each good. (f) What is the MRS? Explain why this example will demonstrate strictly convex indifference curves. (g) Find the indirect utility function v (p, w).There are two goods, X and Y, available in arbitrary non-negative quan- tities (so the consumption set is R²). Beenish has preferences over consumption bundles that can be represented by a differentiable, strictly increasing and strictly quasi-concave utility function u R² → R+, given by u(x, y) = xªy¹-a where x is the quantity of good X, y is the quantity of good Y, and a € (0, 1) is a preference parameter. = 1. Suppose Beenish has 80 AED. In a nearby store (called "Store A"), the price of good X is p = 2 AED per unit of good X, and the price of good Y is q 8 AED per unit of good Y. However, Beenish also has a time constraint. At Store A, it takes tx 4 minutes per unit to purchase good X and ty 1 minutes per unit to purchase good Y. That means, purchasing a consumption bundle (x, y) = R² at Store A would take 4x + y minutes. Beenish has only 80 minutes to do her shopping. = (a) In an appropriate diagram, illustrate Beenish's constraint set, given that she has both a monetary…QUESTION ONE The only source of income available to Doreen, a level 200 student of UEW is her monthly stipend (M) from her parents. She neither saves nor borrows. Assuming she spends all her income on only two goods food (F) and Clothes (C), with Pr and Pc being the prices of the two goods respectively and having a utility function of the form: U = 6F°C i. Write an expression for Doreen's budget constraint. ii. Assuming good Fis on the vertical axis, produce a sketch of her budget constraint and determine the slope. iii. Find Doreen's monthly equilibrium demand functions for both goods. iv. With Pr and Pcgiven as ¢12 and ¢15 respectively and income of ¢300, calculate the equilibrium quantities of both goods. v. Compute the price elasticity of demand for both goods and interpret your results. vi. If income and prices of the two goods increase by 50%, calculate the equilibrium quantities of Food and Clothing.
- he Calculus of Utility Maximization and Expenditure Minimization -End of Appendix Problem uppose that there are two goods, X and Y. The price of X is $2 per unit, and the price of Y is $1 per unit. There are two onsumers, A and B. The utility functions for the consumers are UA(X,Y)= X05.05 UB(X,Y)= X0.8y0.2 Consumer A has an income of $100, and Consumer B has an income of $300. Using Lagrangians, solve for the optimal bundles of goods X and Y for both consumers A and B. a. The optimal bundle for consumer A is X = 25 and Y* = 50 - b. The optimal bundle for consumer B is X = 120 and Y* = 60How a demand curve can be derived with budget constraint- indifference curve framework? ExplainDraw the following scenario: Muhammad's percelves canned tuna (Y) as an inferior good and fresh tuna (X) as a normal good. If his income Increases by 100%, and his Income elasticity of both types of tuna is 1. Show the effect of this increase in income on the change in his optimal choice of canned and fresh tuna, highlighting his income-consumption curve. Clearly label your graph. Reflect the proportional changes in your graph. The graph may be something like that
- Question 1 Consider an economy with two goods t = 1, 2. Whenever an individual consumes x1 units of good 1 and x2 units of good 2, their utility is given by u(x1 ,x2 ) = lnx1 +δlnx2 , where δ is a parameter taking values 0 < δ < 1. (i) How does the parameter δ affect the marginal rate of substitution between goods 1and 2? Explain intuitively how does the relative preference for goods 1 and 2 change as the parameter δ increases.Pankti consumes two goods, x and y. Her utility function is given byU(x, y) = ln(xy).(a) Are Pankti’s preferences homothetic? Explain.(b) Suppose when Pankti’s income is 12, her optimal bundle consists of 2 units of x and 6units of good y. Without solving for Pankti’s Marshallian demands for x and y,determine how her consumption of x and y would change if her income doubled(holding constant the prices of the goods). Justify your answer as well as you are able.(c) Find an expression for Pankti’s indirect utility function, V (px, py, m), using themethod of Lagrange multipliers. Confirm your answer to part (b) using theMarshallian demands you derive in the process of solving the optimization process.(d) Suppose the price of good x is 2 and the price of good y is 2. Find Pankti’s utilitywhen her income is 24. Now suppose the price of good x doubles to 4. How much extraincome does Pankti need to obtain the same level of utility she had prior to the priceincrease?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.