Because Income depends on work effort and work effort depends on nutrition, suppose the relationship between income (Y) and total food availability (F) in a poor household is given by: Y = 10F + 20F2 – 0.6F3
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Because Income depends on work effort and work effort depends on nutrition, suppose the relationship between income (Y) and total food availability (F) in a poor household is given by:
Y = 10F + 20F2 – 0.6F3
a) If food availability in a two-person household is 20, would it be “rational” to share the food? Explain.
b) If food availability in a two-person household is 30, would it be “rational” to share the food? Explain.
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- Sam's extended family spends $3,200 per month on wine and beer. Their utility function is given by U = 200WB, where W represents the number of bottles of wine that they buy, and B represents the number of cases of beer that they buy. Wine costs $25 per bottle and beer costs $32 per case. Sam's family wants to maximize their utility. Calculate how many bottles of wine and how many cases of beer they should buy. Show your calculation(s).6.8 (0) Casper consumes cocoa and cheese. He has an income of $16. Cocoa is sold in an unusual way. There is only one supplier and the more cocoa one buys from him, the higher the price one has to pay per unit. In fact, r units of cocoa will cost Casper a total of x² dollars. Cheese is sold in the usual way at a price of $2 per unit. Casper's budget oquation, therefore, is a² + 2y = 16 where r is his consumption of cocoa and y is his consumption of cheese. Casper's utility function is U (xr, y) = 3r + y. (a) On the graph below, draw the boundary of Casper's budget set in blue ink. Use red ink to sketch two or three of his indifference curves. Cheese 16 12 8 0 4 8 12 16 Cocoa (b) Write an equation that says that at the point (r, y), the slope of Casper's budget "line" equals the slope of his indifference "curve.". Casper demands units of cocoa and units of cheese.Because Income depends on work effort and work effort depends on nutrition, suppose the relationship between income (Y) and total food availability (F) in a poor household is given by: Y = 10F + 20F2 – 0.6F3 a) If food availability in a two-person household is 20, would it be “rational” to share the food? Explain. b) If food availability in a two-person household is 30, would it be “rational” to share the food? Explain.
- A basket of goods for a given consumer includes two goods, X and Z. Consumer income is equal to $1,500 and the prices of these two goods are as follows: P= $20 P, = $25 This consumer is consuming 10 units of good X. Suppose that over the course of a year, the price of good X changes by 10% and the price of good Z changes by - 10%. How much income would be required for the consumer to afford the same quantity of goods X and Z with the new prices? SSuppose we want to fairly allocate a set of indivisible chores, for which each agent has negative utility. What is the natural analogue of EF1 allocation in this case? Design an algorithm to obtain an EF1 allocation when agents have additive valuations.Suppose the government implements an income support program with the intention of making sure residents are able to purchase sufficient food. The government pays a cash benefit to all individuals with incomes less than $1000 according the following formula: cash benefit (CB) = $200 – 0.2*(earned income(I)) Households spend all of their income on food (F) and other goods (X). The price of food and other goods are normalized to 1. A households budget constraint is F + X = CB + I Households have the following preferences: U = 0.25*ln(F) + 0.75*ln(X) Refer to Scenario 3 Suppose a household has earned income of $300 and instead of cash, the government benefit is in the form of food stamps, or vouchers, that must be spent on food. How much does the household spend on food now?
- A consumer is choosing between magazines and books. His set of consumer optimums are shown on the graph to the right. 50 Consumer income allocated for these two goods is equal to $150. The price of 45 magazines (P,) is equal to $5.00. 40- How do these changes in the price of books affect the demand for magazines? 35- 30- 25 NN 20- demand remains constant 15- PCC demand increases 10- 5- demand decreases 0- Ó 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Books étv 21 MacBook Air 80 DII F5 F6 F7 F8 F9 F10 F1 F2 F3 ! @ $ & * 1 2 3 4 6. 7 Q W E T U A S F H. J K L C V M option command command op ...- * C0 Magazines DSuppose a family (with 1 child) earns $50,000 per year and there is no publicly provided education. Assume the price of other goods is $2,000 and the price for education/ year is $5,000. Show how a school voucher redeemable for $20,000 worth of education changes the family's budget constraint. What happens to the amount of education the family purchases for the child?The graph below shows the budget constraint between income and leisure for an individual. The individual has a total of 4000 hours to divide between working and leisure for the entire year. The maximum an individual could make by working all 4000 hours is $20,000. For every hour spent in leisure, one less hour is spent working and vice versa. Suppose that, as illustrated in the graph, a government antipoverty program guarantees the individual $10, 000 in income per year. As the current government support is too low to help individuals out of poverty, the government has decided to increase the government support to $22, 000 per year. The individual is no longer motivated to work any hours as it is not possible for him/her to make more income than the guaranteed government support. Move the Government Support line to illustrate this outcome. Provide your answer below: 30000 25000 (0, 20000). 20000 15000- Government Support ($10000) 10000 5000 (4000, Q) 2000 4000 3000 Leisure (Hours) 1000…
- Jen from Thunder Bay consumes housing (H) and food (F). Her studentstipend is $600/month. She has a utility function of U(H, F) = F1/3H2/3.The initial price of food is pF = 1 and the price of housing is pH = 10. (a) Determine how much food and housing she consumes.(b) Suppose the government decides to subsidize her housing by 50%.This has the effect of lowering the price she actually pays for housingto $5. If the price of food is $1 and the price of housing is $5, calculateJen’s utility maximizing bundle of goods.(c) How much does the Government spend on this program (just on Jen)?(d) Calculate her utility level using the utility function above and thequantities consumed.(e) Calculate Jen’s utility maximizing bundle and her resulting utilitylevel if the government chooses to simply give her the money theywould have spent on the program (rather than subsidize housing).How much utility does Jen get?(f) Given the two programs cost the same, which one is better for Jen?Illustrate the…EXERCISE 7 Aisha is considering how to allocate the next 6 hours of her free time. She could choose between leisure (L) and helping her neighbour with the house chores. If she decides to help her neighbour, she is going to get paid at £25 per hour, which she can then spend on her favourite pizza (P). Suppose the price of pizza is £12.50. Aisha's preferences for leisure and pizza are given by the following utility function: U(L, P) = 3L + P. (MU₁ = 3, MUp = 1). a) Write down Aisha's budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. b) Calculate Aisha's marginal rate of substitution between leisure and pizza. Explain the concept of MRS and interpret the figure obtained. c) Find Aisha's optimal consumption bundle, both algebraically and graphically. Explain your reasoning. d) Would Aisha's optimal choice change if she could get a discount on her pizza purchases so…Task 4: leisure or work? The consumer choice is not restricted to the choice of consumption goods. In fact, it can apply to all our decisions that involve trade-offs. Suppose Mary has a wage per hour of 10 euros. With her earned income she consumes. That is, C = wH per day. She also decides how many hours to work of take leisure time each day. H = 24 – N, where H is work and N is leisure. Her utility is given by C1-o U(C, N) + B log(N) 1- o (a) Solve for the optimal decision of labor/leisure. Plot the budget constraint and the indif- ferent curve. What is the labor supply function? (b) If o > 1, what is the shape of the labor supply? How does it relate with the income and