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A consumers utility function is given by U(X1, X2)=Xa1X21-a where A>0, 0<a<1 A consumer also faces the prices p1 and p2 and has income levels. Obtain the consumers demand functions X1 and X2 as well as the indirect utility function of the consumer
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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 consumers utility function is given by U(X1, X2)=Xa1X21-a where A>0, 0<a<1 A consumer also faces the prices p1 and p2 and has income level m. Obtain the consumers demand functions X1 and X2 as well as the indirect utility function of the consumerLet a1 and x2 denote the quantities consumed. The consumer's preferences are represented by the utility function: U (r1, 22) = V+ VT2. Suppose the consumer has income m =100 and that the prices for the two goods are pi -2 and p2=8. Calculate the optimal quantity demanded for good 1.
- A consumer has the following utility function: U(X,Y)= 400X2/5Y3/5 Suppose that the price of a spa day (x) is £200 and the price of a city break (y) is £300 Find the number of spa days and city breaks that minimise expenditure if 12,800 units of utility are obtained. Also calculate the consumer's minimised expenditurePlease answer all the questions below. A consumer’s preferences over two goods x and y are given by the utility function U(x, y) = min{αx, y} with α > 0. The prices of the goods are px = 2 and py = 1. The consumer has an income of I > 0.(a) For what values of α is this utility function strictly monotone? (b) For what values of α will the consumer demand (i.e., Walrasian demand) be more x than y? (c) For what values of α will the consumer spend more on x than y (given her Walrasian demands)? (d) If x is bicycle tires and y is bicycle frames, then what is the reasonable value for α? Given px, py and this value of α, what is the minimum cost of obtaining a utility u = 1? What are the demands that solve this expenditure problem?A 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 $25 and the price of Pizza does not change. Compute and represent graphically the new equilibrium of the student. What can you tell about the substitution effect on Salad and pizza
- A consumer derives utility from two goods (x and y), and her utility function is in the form u(x,y) = xy. Her income is 120 TL, and the prices of x and y are both 1 TL: a) Find the quantities of x and y that maximizes her utility. b) Derive the demand functions for x and y.Consumer has the following utility function U(x,y) = x1/2y1/2 , where the price of good x is 1$ per unit, the price of good y is 4$ per unit, and the consumer’s income is 800$. Find the utility maximizing consumption levels of x and y.A consumers utility function is given by U(X1, X2)=Xa1X21-a where A>0, 0<a<1 A consumer also faces the prices p1 and p2 and has income level m. Set up the expenditure minimization problem and find the expenditure function E(p,u)
- 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)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 has preferences represented by the utility function: with 0 < a < 1. U (x₁, x2) = aln(x₁) + (1 − a)ln(x₂) (a) Derive demand functions (optimal choice of x1 and x2 as a function of income and price(s)). (b) Derive price and income elasticities.