Irene spends all of her income M on soda and chips. The price of soda is 2 per unit. Irene’s utility function is U (s, c) = 5 ln(1 + s) + ln(1 + c). (a) Derive Irene’s demand function for chips (as a function of her income and the price of chips).
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Irene spends all of her income M on soda and chips. The price of soda is 2 per unit. Irene’s utility function is
U (s, c) = 5 ln(1 + s) + ln(1 + c).
-
(a) Derive Irene’s demand function for chips (as a function of her income and the price of chips).
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- a)Assume that the typical consumer always spends a small share of her overall budget on Vietnamese meals and use the utility maximization conditions to find the demand for Vietnamese food of the typical consumer (keep in mind that since utility is quasi-linear, you can find demand without information about the consumer’s weekly budget). b) Sum across consumers to find the weekly market demand for Vietnamese meals in NYC.Jennifer buys both turkey (x) and cheese (y) for her sandwiches. Her preferences over these two goods can be represented by the utility function U(x,y) = min[x, 2.5y] where x represents the number of slices of turkey and y represents the number of slices of cheese. a) Given her preferences find her demand functions for turkey (x) and cheese(y).Define Economic utility
- 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 pizzaQuestion 3 Utility Maximization Marge has the utility function U(F,H)=20F?H where F is the quantity of footwear and H is the quantity of hats she consumes. Suppose the price of footwear is $20 and the price of hats is $5, while Marge has an income of $200/week. 1. Calculate Marge's MRS as a function of the quantities F and H. 2. BONUS: Write down the Lagrangian function for Marge's utility maximization problem. 3. Solve for Marge's optimal consumption bundle of footwear and hats, You can either use the Lagrangian from part b or use any other method you likeliKhamzat consumes burgers (x1) and sodas (x2). Consider the CES utility function u(x1, x2) = (x + x)UP), for a constant p > 0, where the price of burgers is 20 and soda is 2. Khamzat's income is 100. What is the demand functions for burgers and sodas? Khamzat becomes famous and the store owner recognizes him and decides to give him the burgers at cost, $12. What is the income and substitution effect?
- Anna has an income of 1000 euros and utility function U(x,y)=x²y³. The prices of the two goods are P₁=5 and Py-20. a) Define the budget constraint and represent it graphically. (Utility maximization with a budget constraint. A hypothetical consumer spends all tgheir income on ramen noodles (N) and wild rice (W). N is the quantity of noodles; W is the quantity of wild rice. Their income is $1,600 per month. the price of noodles is $2 per package and the price of wild rice is $20 per pound. The utility function is U=sqrt(N*W). the MRS = -N/W. The budget constraint is: 1,600 = 2*N + 20*W Graph Qty of noodles (N) on vertical axis and Qty of wild rice (W) on horizontal axis. SOLVE: a. Graph the budget constraint. label all points. What is the slope of the budget constraint? b. Find the optimal quantities of noodles(# of packages) and the wild rice (# of pounds) given the budget constraint. graph these optimal quantities. draw your indifference curve on the same graph. c. Show on your graph what happens when the price of wild rice increases to $40 per pound. Find your new optimal quantities of noodles and wild rice. label all points on graph. label the…Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Suppose that the Department of Welfare wants to know how much should begiven to Eren to offset his change un utility due to the price increase of an expensivemeal. Calculate the compensative variation (CV).
- Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate for the equivalent variation (EV) for the price change.Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate the change in consumer surplus from consuming the expensivemeals considering the price change (Hint: you need to compare his optimalconsumption bundle before and after the price change to get the change in CS).You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.