10. Omar has Cobb Douglas preferences for Juice (X1) and Soda (X2). His MRS at his optimal consumption is 2. If the price of juice is p1= $6. What is the price of Soda, p2?
At the optimal consumption,
MRS = price ratio ( Price of juice / Price of Soda)
Put values, we get
MRS = p1/ p2
2 = 6/ p2
p2 = 6/2 = 3
So price of Soda, P2 = $3.
10. Omar has Cobb Douglas preferences for Juice (X1) and Soda (X2). His MRS at his...
Please do all the parts and explain it well Priya has Cobb Douglas preferences for Juice (X1) and Soda (X2). Her MRS at his optimal consumption is 2. If the price of juice is p1= $6. What is the price of Soda, p2?
1. A buyer has Cobb-Douglas preferences such that mrs = − x2/ x1 . He starts with 3 units of good 1 and $50. Use this information to answer the following questions. (a) Find an expression for this consumer’s net demand for good 1 (i.e. how many more units he will buy given price p). (b) Sketch this demand curve. (Make sure you label the axes and put p on the vertical axis.)
1. Student A has preferences represented by U(x1,x2) = min{ax1,bx2}. Suppose good one has a special tax. The government wants good one to be consumed as little as possible, so it imposes a tax on its price when more than x units are bought. Specifically, the price of good one is p1 if less than x units are bought and it is p1(1 + t) when buying more than x units (for all the units bought). Where t indicates the...
QUESTION 11 Suppose there are two goods, X1 and x2, and your preferences are represented by the following utility function: , u(x1,x2) = x1/4xz.! The price, P1, for good x1, is 2.5 and the price, P2, for good x2, is 3.5. You have units of money (M) of 60. Compute the consumer's optimal consumption of x1and x2 Enter x1 only here:
2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his preferences are represented by the Cobb-Douglas utility function U(x1, x2) = x1 c x2 d , where c>0 and d>0. State Bob’s optimization (utility maximization) problem. a) Set up the Lagrangian function. b) Derive the necessary conditions (the first-order conditions) for an optimal interior solution. c) Show that the MRS (the slope of the indifference curve) is equal to the slope of the budget...
2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his preferences are represented by the Cobb-Douglas utility function U(x1, x2) = x1 c x2 d , where c>0 and d>0. State Bob’s optimization (utility maximization) problem. a) Set up the Lagrangian function. b) Derive the necessary conditions (the first-order conditions) for an optimal interior solution. c) Show that the MRS (the slope of the indifference curve) is equal to the slope of the budget...
Assume that a consumer’s preferences are given by u(x1, x2) = 10x11/2 * x21/2 Currently, m = 200 and p1 = 10 and p2 = 20. Suppose now that p1 increases to p'1 = 20. What is the total effect of this price change in the optimal consumption of the two goods for the consumer, and what are the substitution and income effects? Step 1:Solve the consumer’s problem given her preferences (described by u) and under the assumptions that m =...
Luke's choice behavior can be represented by the utility function u(x1,x2)= x1 + x2.The prices of x1 and x2 are denoted as p1 and p2, and his income is m. 1. Draw at least three indifference curves and find its slope (i.e. MRS). Is the MRS changing depending on the points of (x1, x2) at which it is evaluated, or constant? 2. Draw a budget constraint assuming that p1 < P2. Find the optimal bundle (x1*,x2*) as a function of income and prices. 3....
1.) Liz has utility given by u(x2,x1)=x1^7x2^8. If P1=$10, P2=$20, and I = $150, find Liz’s optimal consumption of good 1. (Hint: you can use the 5 step method or one of the demand functions derived in class to find the answer). 2.) Using the information from question 1, find Liz’s optimal consumption of good 2 3.) Lyndsay has utility given by u(x2,x1)=min{x1/3,x2/7}. If P1=$1, P2=$1, and I=$10, find Lyndsay’s optimal consumption of good 1. (Hint: this is Leontief utility)....
Assume that a consumer’s preferences are given by u(x1, x2) = 10x11/2 * x21/2 Currently, m = 200 and p1 = 10 and p2 = 20. Suppose now that p1 increases to p'1 = 20. What is the total effect of this price change in the optimal consumption of the two goods for the consumer, and what are the substitution and income effects? Step 1:Solve the consumer’s problem given her preferences (described by u) and under the assumptions that m =...