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- Consider the following utility function belonging to “Consumer A”. UA(x,y,z,v) = x0.1y0.2z0.3v0.4. Suppose that prices of x, y, z and v are 1$, 2$, 3$ and 4$. The consumer’s income is 10$. a. Find the values of x, y,z and v that maximize the consumer’s utility subject to his/her budget constraint. b. Suppose that “Consumer B” has a utility function which is a logarithmic transformation of the consumer A’s utility function, i.e. UB =ln UA. Suppose that prices and income are the same. Would the amounts of x, y, z and v consumed by “Consumer B” be the same as the amounts consumed by “Consumer A”?Suppose a consumer purchases food X and clothing Y. The utility function of the consumeris given by: U(X,Y ) = XY + 5Y and the budget /income/ of the consumer is 200 ETB. Andalso the price of food is X P and the price of clothing is Y P . Then drive the equation ofconsumer’s demand function for food and clothing.An individual’s utility function is given by U = 900x1 + 500x2 + 6x1x2 − x21 − x2/2.When the weekly amount of leisure is x1 = 140 and earned income is x2 = 800 answer the following: (a) What is the marginal utility of x1 ? (b) What is the marginal utility of x2 ? (c) Use the small increments formula to estimate the change in the utility when x1 decreases by 1 and x2 increases by 4. (d) Does the law of diminishing marginal utility hold? (e) What is the MRCS at a given values?
- Assume that a consumer has two goods to consume: medical care services (M) and all other goods (X). She has monthly income of $4000. a. Plot how the budget constraint should change when this consumer’s income increased to $8000. Remember to label the origin, axis, and intercepts on your graph.The relationship between a consumer’s income and the quantity of X, he consumes is given by the equation M=1000Q2A student has a lunch utility function U(S, P) 8S + 3P, where S is number of salads per month and P is number of pizzas per month. The price of a salad is $5, the price of a pizza is 8, and his monthly income for lunch is $80. a) Derive the equation representing the consumer's demand for Salad. Represent the demand for Salad graphically. b) The price of Salad goes up to $25 and the price of Pizza does not change. Compute and represent graphically the new equilibrium of the student. What can you tell about the substitution effect on Salad and pizza
- A consumer has product happiness function c1*c2.When this consumer eats 5 apples and 3 bananas, they get a happiness level of ______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.Q: A consumer’s preferences for food (F) and clothing (C) are given by U(F,C) = F0.2C0.8. The price of food is $4, and the price of clothing is $8. The consumer has an income of $3600. a) What is the utility maximizing choice of food and clothing? b) How would the utility maximizing choice change if price of clothing increased to $14? c) Given the answers to the previous parts plot a linear approximation to the demand function for clothing.
- 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.Assume there is consumer, his utility function is U(x,y)=y/(100-x). If px = 1, py = 1, please show the demand function of x (as a function of m), and draw the Engel curve (the graph showing the relationship of m and the demand of x)A consumer has set a budget of $600 for the consumption of good X and Y. The price of Good X is $20, and the price of good Y is $10. The consumer has a Utility function given by UCX. Y) = x0.60, 0.40 a) Find the optimal solution using a method that does not involves equations and illustrate the.