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- The demand for Peet's Coffee over a week should be more elastic than the demand for Peet's Coffee over a year. True False5. A consumer's utility function is U = In x, +2 In x2 Find the values ofxi and x2 which maximize U subject to the budgetary constraint 2x, + 3x; = 18QUESTION 1 For the utility function U = (Qx0.5+Qy0.5)² and the budget 133 = 8Qx + 10Qy find the CHANGE in optimal consumption of Y if the price of X increases by a factor of 1.1. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14 = 1.1).
- 1. In a simple but delicious world, Joey eats only sandwiches, s, and jam, j. He has a Cobb-Douglas utility function U(j, s) = Nj1-asª, where 0 0. The price of jam is pj, the price of sandwiches is Ps, and Joey has a monthly budget Y to spend on lunch. a. Explain why you can safely use a simpler Cobb-Douglas utility function, V(j, s), to represent Joey's preferences, which is the same as U(j, s) except for replacing N with 1. b. Transform V(j,s) by taking natural logs and bringing down exponents. Explain why it is useful to do this for a Cobb-Douglas utility function, but not for a quasi-linear utility function. Use In(V(j, s)) and the substitution method to derive the formulas for Joey's optimal amount of jam, j*, and sandwiches, s*, to buy and consume per month. Simplify your answers so that you arrive at the С. (1-a)Y aY formulas j* = and s* Ps d. What fraction of his income does Joey spend on jam, and what fraction on sandwiches?B.3 Marie has preferences over two goods, cake q₁ and bread q2. She chooses quantities to consume so as to best satisfy these preferences subject to the budget constraint p1q1 + P292 y where p₁ and P2 are prices and y is total budget. Suppose that Marie's preferences are represented by utility function u(q1, 92) = 91 + In (bq1 +92) where b≥ 0 is a preference parameter. Assume that p1/bp2 ≥ y/ (P1 - bp2) ≥ 1. (a) Show that Marie's indifference curves are downward sloping and that her weakly preferred sets are convex for all possible values of b. (b) Show that her Marshallian demand for cake gi is Y fi (y, P1, P2) 1 P1-bp2 and find her Marshallian demand for bread, f2 (y, P1, P2). Discuss the shape of Engel curves for the two goods. (c) Explain why Marshallian demand curves for normal goods slope down. Are there any values of b for which either cake or bread could be a Giffen good for Marie? Discuss. (d) Find the form of the indirect utility function and expenditure function and hence…= x 2 y. This Consider a consumer with the utility function U (x, y) = Vxy 글3글2-iy and MU, Vx = x? They have 1 function gives MU Va a budget of $60, and pr 1 and Py 2. Find optimal consumption of x and y.
- Economics Summer break is approaching! Suppose you derive utility from days spent traveling on vacation domestically, D, and days spent traveling on vacation in a foreign country, F. Your utility function over these two “goods” is: U(D, F) : 4D0.25F 0.75 Let your budget constraint be I(D, F) = pDD + pF F; where I is your income, pD is the price of domestic travel per day, and pF is the price of foreign travel per day. a. Determine the demand functions for domestic travel and foreign travel. Make sure you show your work – show the steps used. b. Suppose that you’ve saved $800 for your summer travel, the price of domestic travel per day is $25 and the price of foreign travel per day is $100. How many days of each type of travel will you embark on? c. Illustrate the indifference curve, budget constraint, and the utility maximizing bundle associated with (b). Make sure you show the level of utility, the budget constraint intercepts, and the optimizing equilibrium. Your answerFocus on parts e-hAnthony seeks to maximize the following utility function u(x, y) = x'/3y2/3 subject to the budget constraint Pæa + PyY = I 1 where pr, Py, x, y, I > 0. a) Find Anthony's utility-maximizing bundle (x*, y*) as a function of pæ, Py, and I. b) Show that y* is decreasing in py and increasing in I (hint: use partial derivatives). c) What share of Anthony's income is spent on x? What share is spent on y? In other words, calculate Pa and Pu. Are these shares a function of prices? Pyy* Note: The above utility function is Cobb-Douglas, and all Cobb-Douglas functions have these share formulas for any values for the exponents. d) What is the impact of a change in pr on Anthony's utility?
- Please answer fast arjent pleaseFor the utility function U = (Qx0.5+Qy0.5)² and the budget 122 = 8Qx + 8Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.7. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).Suppose Mia's utility function on lemon soda (X) and chips (Y) is given by U(X,Y) = X0.5Y0.5 She has $80 per month to spend on lemon soda (X) and chips (Y). The prices of lemon soda (PX) and chips (PY) are $2 and $4 respectively.a. Solve for her optimal consumption bundle of lemon soda (X*) and chips (Y*)? i. Optimal Consumption in lemon soda (X*) : ii. Optimal Consumption in chips (Y*) : b. Suppose the price of lemon soda (X) increases to $8, what is the new optimal bundle? i. Optimal Consumption in lemon soda (X*) : ii. Optimal Consumption in chips (Y*) :