Problem 1 - Consumer Choice Consider the case of a consumer who decides how many cups...
Consider the case of a consumer who decides how many cups of coffee (denote by c) and cups of tea (denote by t) to consume every month. Assume the income endowment for caffeine needs is $300; the price of a cup of tea is $2 and the price of a cup of coffee is $3. a) Write down a Cobb‐Douglas utility function with exponents α=0.5 and 1‐α=0.5. b) Write down the budget constraint for this problem. c) Set up the...
Consider the case of a consumer who decides how many cups of coffee (denote by c) and cups of tea (denote by t) to consume every month. Assume the income endowment for caffeine needs is $300; the price of a cup of tea is $2 and the price of a cup of coffee is $3. a) Write down a Cobb-Douglas utility function with exponents a=0.5 and 1-a=0.5. b) Write down the budget constraint for this problem. c) Set up the...
Consider the typical example of shopping at Walmart for pants (x1) and shirts (x2). Your income endowment is $300; the price of shirts is $20, and the price of pants is $30 a) Write down a Cobb-Douglas utility function with exponents a=0.5 and 1-a=0.5. b) Write down the budget constraint for this problem. c) Set up the Lagrange and find the optimal consumption bundle for Xi and x2 (call this bundle A) d) Now assume that the price of pants...
4. Malachi only consumes 2 goods: DVD rentals and coffee. His utility function is U(R,C)=R0.4C0.6 where R is the number of DVD rentals and C is cups of coffee. Malachi has $30 in his pocket right now, and he plans to spend all of the money on rentals and coffee today. a. The price of one rental is $3 and the price of one cup of coffee is $2 per cup. Solve for the optimal bundle. b. Suppose that Malachi...
4. Malachi only consumes 2 goods: DVD rentals and coffee. His utility function is U(RC)-Rº4CO6 where R is the number of DVD rentals and C is cups of coffee. Malachi has $30 in his pocket right now, and he plans to spend all of the money on rentals and coffee today. a. The price of one rental is $3 and the price of one cup of coffee is $2 per cup. Solve for the optimal bundle. b. Suppose that Malachi...
Happy Goluki likes tea (good 1) and cookies (good 2) Her preferences are represented by the utility function U(q1,q2) (q1)05(q2)0.5, where q1 is the number of cups of tea and q2 is the number of cookies Goluki is given I-$180 that she is allowed to spend as she wishes on tea and cookies. a) Calculate Goluki's optimal bundle if the price of tea is p1=$1 and the price of cookies s p2 $2. Call this bundle A and show it...
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...
only question that is problem is (i) many thanks . Problem 1 [32 marks] A consumer has a demand function for good 2, X, that depends on the price of good I. P. the price of good 2. Pz, and income, m, given by xy = 2+ +2P. Initially, assume m= 40, P-1, and P = 2. Then the price of good 2 increases to P = 3. a) What is the total change in demand for good 2? [2...
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...
Suppose that a consumer has a utility function given by u(x1, x2) = 2x1 + x2. Initially the consumer faces prices (2, 2) and has income 24. i. Graph the budget constraint and indifference curves. Find the initial optimal bundle. ii. If the prices change to (6, 2), find the new optimal bundle. Show this in your graph in (i). iii. How much of the change in demand for x1 is due to the substitution effect? How much due to...