Suppose that a consumer had a utility function given by: U=X²Y4. This consumer has a budget of $12. Fill in the value of this consumer's demand function. X = *(1/Px). (For instance, if X = 4/Px, then X = 4 * (1/Px) and enter 4)
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Lesson 6- Individual and Market Demand
Question 9
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- Suppose a consumer has the following utility function: U(x1,x2) = alnx1 + (1-a)lnx2. The price of good 1 is $10 and the price of good 2 is $20 and the consumer’s income is $500. Find the quantities of x1 and x2 that will maximize utility if a=1/2.A consumer has utility function U(x1, X2, X3, X4, X5, X6, X7) = min{/x1x2, /X3X4, VX5X6X7} Find the demand function. 3)Suppose a consumer had a utility function given by: U = X²Y0.5. If the price of Good X (Px) is $3 and the price of Good Y is $6 then what is the utility maximizing quantity of Good X the consumer will purchase with a budget of $15? (Round to the nearest decimal place if necessary.)
- Assume a consumer has a utility function U(x1, x2) = x1x2 where x1, x2 represents the amount of two goods 1 and 2 consumed in a given time period, find the utility-maximizing consumption function subject to the budget constraint5x1 + 4x2 <= 50= 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.For each of the following utility functions get the marginal utility of consumption of each of the goods. 1/2 1/2 (a) u(a,b) = a b (b) u(x, y) = x³/4y1/4 (c) u(a, b) = n(a) + In(x) (d) u(x, y) = ln(x) + ln(y) (e) u(a, b) = 2xa +Xb
- A consumer has the following utility function: U(X1,X2) = X1X2 + X1 + 2X2Where X1 is her consumption of candies with a price of $2 and X2 is her consumption of notebooks with a price of $5. Her income is $51. Determine the number of candies andnotebooks that will maximize the consumer’s utility.The utility function of a consumer is u = √x + 2y. (a) Calculate how much MRS of that consumer when x = 4. (b) If the consumer currently consumes 4 units of goods x and the price ratio of Px / Py = 1/4, then the consumer should increase or decrease the consumption of goods x?Anthony 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?
- Suppose a consumer had a utility function given by: U=X0.5Y. If the price of Good X (Px) is $1 and the price of Good Y is $2 then what is the utility maximizing quantity of Good Y the consumer will purchase with a budget of $24?You have the Cobb-Douglas utility function u(x,y) = xy over apples (x) and plums (y) and you have $120 budget to spend and can carry at most 480 ounces in weight in your backpack going back to the dorm. Each apple costs $1 and weighs 8 ounces, and each plum costs $3 and weighs 4 ounces. You can only leave the store with a bundle of fruits you can afford and carry. (a) Drawing the relevant lines, intercepts, marking the points and hence identifying the feasible set of bundles, calculate the optimal bundle. (b) Forget about (a). If you were to choose a backpack before going on this shopping trip, for the weight constraint not to be an issue for you, how many ounces of weight capacity would you need for your backpack? HINT: That is, for this weight capacity of the backpack, you’d be able to carry the best bundle you can afford, i.e, the weight constraint is not binding for your decision. ( c) Forget about (b). In (a), just before going out for shopping with your backpack to buy the…If Ginna spends her entire budget, she could buy a chosen set of groceries and also buy 10 notebooks. If she spends only half of her budget, she could only buy a set of groceries and could not afford any notebooks. Suppose Ginna's budget is £150. Her preferences for groceries (G) and notebooks (N) can be described by the following utility function: U (G, N) = 30G + 2N (MUG = 30, MUN = 2). a) Find Ginna's optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. b) Discuss how the price of a notebook should change for Ginna to change her optimal consumption choice. c) If the price of a notebook increases by 50%, how should the price of the groceries drop so that Ginna can be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Ginna's optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Ginna's demand for groceries and/or notebooks.