True or False: ( ) when AVC curve is ˃ MC curve, then ATC has a negative slope ( ) If MUy / Py ˂ MUx / Px , to reach equilibrium, the consumer must decrease his consumption of y ( ) The ISO-quant curve is convex toward the origin point which illustrates the law of ↓MRTS.
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True or False:
- ( ) when
AVC curve is ˃ MC curve, thenATC has a negative slope - ( ) If MUy / Py ˂ MUx / Px , to reach equilibrium, the consumer must decrease his consumption of y
- ( ) The ISO-quant curve is convex toward the origin point which illustrates the law of ↓MRTS.
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- consumptionA consumer's budget constraint is given by 500 = 40G + 10D, where G is ice cream in liters and D is drink in liters. The consumer thinks that a liter of ice cream is a perfect substitute for 3 liters of drink. Which statements are then correct?Select one or more options: a-2 liters of ice cream and 42 liters of drink are on the budget line b-The optimal choice is to consume 3 times as much drink as ice cream c-The optimal choice is to only consume ice cream d-0 liters of ice cream and 50 liters of drink are on the budget lineAn individual’s utility function is given byU = x1√x2where x1 and x2 denote the monthly consumption of two goods. Unit prices of these goodsare $2 and $4 respectively, and the total monthly expenditure on these goods is $300.(a) Write down the budgetary constraint.(b) Find the optimal quantities of x1 and x2 the maximize U.(c) Verify that the stationary point is a maximum.QUESTION 1 For the utility function U = Qx0.50Qy(1-0.50) and the budget 122 = 8Qx + 14Qy find the CHANGE in optimal consumption of Y if the price of Xincreases 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).
- 0.8 A consumer's utility function is given by the expression: U = (0.6X0.5 +0.4Y0.5) ². Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.Law of equi marginal utility is an important law of cardinal utility analysis. Explain this law with the help of its assumptions. Furthermore, there is a relationship between total and marginal utilities where they both pass through different stages when the consumer continues his or her consumption regularly. Elaborate.= Suppose you are trying to minimize your expenditures E utility level (20.5 + x9.5)² = 175. 4x1 + 3x2 subject to the target maximum • Set up the Lagrangean function for this expenditure-minimization problem with constraint • Compute for the expenditure minimizing quantities of ₁ and ₂. x2. • What is the minimum expenditure you can incur given the level of utility you have to attain?
- 1 Consider a consumer who consumes only two goods, 21 and z2. His utility function is u (21, 22) = In z1 + 2. where In represents the natural logarithm. 1.a Derive the consumer's MRS of good 1 for good 2 using calculus to calculate his marginal utility from z and his marginal utility from z2. 1.b If the price of z1 is $2 per unit and the price of z2 is $4 per unit, and the consumer's income is $100, What is the equation of this consumer's budget line? 1.c What are the optimal consumption choices, z and z5, for this consumer? Show your work.The marginal utilities derived from the consumption of goods X and Y by a given consumer are given by MUx=40-6x and MUy=80-10y. If the prices of X and Y are Gh2 and Gh10 respectfully. determine the number of units of the commodities that the consumer must consume to optimize satisfaction granted that he/she earns an income of GH40 within the period.A9) Suppose we have two goods, x1 and x2, with prices p1 and p2, respectively. Consider the budget constraint X1P1 + X2P2 < m. If both pi and m double (i.e., p’i=2p1 and m'=2m), the area of the feasible consumption set: a) Doubles b) Falls by half c) Stays the same d) Quadruples e) None of the above.
- Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…A consumer consumes two agricultural products: Red Meat, and Tomatoes according to the following utility function: U = RT That is, the total utility is the multiplication of the quantity consumed of the two products. Given that consumer's income is 210, price of R is 10, and the price of Tis 2, a)Write down the budget constraint (budget line equation) for this consumer. b)Determine the quantities that the consumer should consume of each of the two products c)Calculate the value of the lagrangian multiplier and derive the demand function for Red Meat and for tomatoes.Utility maximization under constraint, substitution and income effect, CV and EV Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A, B) = 4[A-4 + B-4-4 + 40. While Josh would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method b. Suppose PA increases. Show graphically the income, substitution effect and total effect and explain c. Suppose PA increases. Show the graphs for CV and EV and explain. One graph for CV and one graph for EV