6. Consider a consumer with the utility function u(x,, x2) = In(x,) + x, and the budget constraint p, x, + P2x2 = m. Derive the consumer's demand functions for x, and x2.
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- A consumer prefers to consume two commodities in fixed proportions. Specifically, she prefers to consume 1 unit of x2 and 4 units of x1 at the same time. Represent her utility function and find the most preferred and affordable consumption bundle for prices p1 and p2A consumer's preferences are represented by the utility function If the budget constraint is P1X1 + P2X2 = M, determine the demand functions q1(P1, P2, M) and Q2(P1, P2, M). Determine also the indirect utility function V(P1,P2,M).Consider the consumer whose tastes and preferences for (X) and (Y) can be characterized by the utility function: U(X,Y) = 2X*Y + 4Y. This consumer has $2,000 to spend and faces prices PX = 5 and PY = 10. The utility-maximizing amount of X to consume is:
- 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 <= 50suppose a consumer consumes two goods x and y with utility function u=x^0.5+y^1.5, does the utility funciton exhibit diminishing marginal utility for (i) x (ii)y?suppose a consumer's utility function is given by U(X,Y) = X*Y. Also the consumer has $288 to spend, and the price of X, Px=16, and the price of Y, Py=1: A. How much X and Y should the consumer purchase in order to maximize her utility?
- Suppose the utility function for a consumer is given by U = X + Y, where X and Y are a consumer's consumption of goods X and Y. Which of the following bundles does this consumer find indifferent between 10 units of X and 5 units of Y? You Answered a. 4 units of X, 10 units of Y b. 2 units of X, 13 units of Y c. 5 units of X, 7 units of Y d. 8 units of X, 8 units of YWhen utility function U(q1, q2)=min{ 34.6 q1, 17 q2} and q1= 33 and q2= 60 are given, find utility level consumer gains?Q 15. suppose the consumer's utility function is given by U(x,y) =x^1/4 y^3/4 where the equation for this consumer's demand curve for x is?
- The consumer's utility function is u(x1,x2) = x1 x2 Graph her budget constraint for P1 = 3, P2 = 2 and M = 900, and write down the equation for her budget Using the MRS= MU1/ MU2 = p11 / P2 tangency condition, find her optimal consumption bundle for these prices and income.For the utility function U = Qx0.46Qy(1-0.46) and the budget 100 = 11Qx + 11Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.5. 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).Given that the marginal utility of X and Y are MUx and MUy respectively, describe the condition for the utility maximizing consumption bundle for a consumer assuming that the price of X is Px and the price of Y is Py.
