need help with exercise 2 and can i have feedback on exercise 1 Exercisel: A consumer...
Question: Consider a consumer with utility function4, income Z, and who faces market prices of p, and py (a) Use our optimality condition of MRSy MRTay to find the relationship between x and y which must always be satisfied by a bundle that maximizes the consumer's utility (b) After incorporating the consumer's budget to the problem, calculate the consumer's de- mand for x and y which we will call x(P Z) and y(Py, Z), respectively, because it empha- sizes the...
1. U = XY where MRS = Y/X; I = 1500, Px = Py = 15, A. Derive optimal consumption bundle. B. If Px increases to be $30, derive the new optimal consumption bundle C. Using the results from A and B, derive the individual demand for good X assuming the demand is linear. 2. Assuming the market has two consumers for a very special GPU and their individual demands are given below Consumer A: P = 450 – 4...
The market for good X consists of 2 consumers. Consumer 1’s demand for good X is: X1 = 15 - 3PX + 0.5PY + .02 *I1 Consumer 2's demand for X is: X2 = 10 - PX + 0.2PY + .01*I2 I1 and I2 are incomes of consumer 1 and 2, respectively. PX and PY are the prices of goods X and Y, respectively. a. What is the equation for the market demand function for X? Graph the two individual...
3. Consider a two consumer endowment economy. Consumer 1 and consumer 2 come into the economy with an endowment of good x and good y. They can voluntarily trade their endowments. They have the following utility functions and endowments: u1(x,y) = zły: u2(z, 1) = a* * And they have the following endowments: Consumer 1 e1 = (4,12) Consumer 2 e2 = = (8,6) (a) Set up the utility maximization problem for consumer 2. Then solve for the demand functions...
Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 3 units of good X and 5 units of good Y. Consumer B is given an initial endowment of 5 units of good X and 3 units of good Y. Consumer A’s utility function is given by: UA(X,Y) = X + 4Y, and consumer B’s utility function is given by UB(X,Y) = MIN (X, 2Y). If the prices...
(Use this information to answer a, b, c below) Suppose Mary’s utility function for two goods X and Y is given by: U(X,Y) = 3X1/2Y1/2 . Suppose consumption bundle A consists of 10 units of X and 30 units of Y, and consumption bundle B consists of 40 units of X and 20 units of Y. a. Consumption bundle A lies on a higher/lower/same indifference curve than consumption bundle B. Show computations. b. Compute Mary’s MRSxy at consumption bundle A....
Bnnas O al UI IImelioRO0d T0l DClla! Eplalli. 2. Suppose that a consumer has utility U(X, Y) goods X and Y a) The prices of X and Y are S1 and $2 per unit respectively. Use a Lagrangian to solve for the optimal basket of goods. b) Suppose that the price of X increases to $2 per unit. Use a Lagrangian to solve for the new optimal basket of goods. Find the total effect of the price change on the...
Consider the following utility function of 3 goods, x, y and z: U(x,y,z)=ax+by+cz; x,y,z≥0 and a, b, c are constants. The prices of good x and y is denoted by pX and pY respectively. The income is denoted by m. Good z is provided by the government free of cost but the quantity of good z provided by the government depends on the consumption of good x and y chosen by the consumer. For example, if in equilibrium, the consumer...
A consumer must divide $600 between the consumption of product X and product Y. The relevant market prices are Px = $10 and Py = $40. (LO2) a. Write the equation for the consumer’s budget line. b. Illustrate the consumer’s opportunity set in a carefully labeled diagram. c. Show how the consumer’s opportunity set changes when the price of good X increases to $20. How does this change alter the market rate of substitution between goods X and Y?
A consumer buys two goods, good X and a composite good Y. The utility function is given as U(X, Y) = 2X1/2+Y. The demand function for good X is X = (Py/Px)2. (Edit: The price of X is Px, the price of Y is Py.) Suppose that initially Px=$0.5 and then it falls and becomes Px=$0.2 Calculate the substitution effect, income effect, and the price effect and show the answer graphically.