5. Consider a monocentric model with fixed housing unit h and the utility of residents u=c, where c is the consumption of the composite goods. The budget constraint of each resident living at distance d from the CBD is c + ph = w-dt, where w is wage, p is housing rental rate, t is the unit commuting cost in distance. The city is open and free migration in and out. The external utility they obtain out of the city is ū= 10. The rental rate on agricultural land is pA. (a) Illustrate why the consumption of residents living in all parts of the city will be equalized. (b) Derive the housing rental rate (p) as a function of d, distance from the CBD, What is the slope? Draw a figure with p at the y-axis and d at the x axis. (c) Discuss how the boundary of the city is determined in this model, how would the boundary of the city respond to wage w and commuting cost t?
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- 7. An individual's utility function is given by U =1000x, +450x, +5 x,x, -2x - x where x, is the amount of leisure measured in hours per week and x, is income earned measured in cedis per week. Determine the value of the marginal utilities, when x, = 138 and x, = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?1) Sharon spends her time (20h) between leisure (L) and work and he consume Y product from his working income (Py=1). Assume that she gets W$ per hour of working and has the following utility function: U (L, Y) =LY+2L C. vv). e. VS What will happen to L, Y and H if the wage per hour (W) will decrease? d. How would your answer to the previous question (c) will change if Sharon has a fixed amount of money (Wo) that is not connected to W? If Sharon has the following utility function: U= L³+ Y², is it possible that she will choose not to work at all? Explain and show the condition for your result if exists. |||2. a. Draw the daily budget constraint of a consumer who has 24 hours in their day, and can earn a wage of $20 an hour for every hour chosen to work (and not consumed as leisure). They can spend their income on a composite good c that costs $8 per unit. This consumer also receives $100 from their supportive parents every day. b. If this consumer's utility function for leisure (r) and c is given by U (r, c) = rc, calculate this consumer's optimal bundle.
- In 2002, a French law went into effect that cut the standard work week from 39 to 35 hours (workers got paid for 39 hours even though working 35), while at the same time prohibiting overtime hours from being worked. (Overtime in France is paid at 25% above the normal wage rate.) (a) Draw the old budget constraint, showing the overtime premium after 39 hours of work. (b) Draw the new budget constraint. (c) Analyze which workers in France are better off under the 2002 law. Are any worse off? Explain. I need help with part(c) Please do not copy answers from other websites.In the short run, Multiple Choice TVC will increase for a time at a diminishing rate, but then beyond some point will increase at an increasing rate. TVC will increase for a time at an increasing rate, but then beyond some point will increase at a diminishing rate. TVC will increase by the same absolute amount for each additional unit of output produced. one cannot generalize concerning the behavior of TVC as output increases.5. A consumer's utility function over leisure and consumption is given by u(L, Y) = LY. Wage rate is w and the price of the composite consumption good is p = 1. (a) Suppose w = 10. Find the optimal leisure - consumption combination. (b) Suppose the overtime wage law is passed so that the firm must pay 1.5 times the normal wage for hours worked beyond the first 8 hours. Find the effect on the hours worked. Decompose the effect into substitution effect and income effect.
- Marley has 100 hours per week available she can spend either working or doing leisure activities. He can work at a wage rate of $50 per hour. Bob receives $1000 of rental income per week, no matter how much he works. Use leisure-income model to solve this:- i) draw Marley budget line and optimal choice of working 80 hours in a week then calculate the maximum and optimal amount of income ii.) And suppose Marley is suppose to share the household expenses and then be taxed 50% of her wage income. then draw another diagram to compare Marley choice in Part i) and the new labour supply decision of working 90 hours per week due to the tax. Clearly label out the income effect, substitution effect and total effect in the diagram.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 andProblem Set 1. A firm's production function is º=50L-0.01Ľ' , where L denotes the size of the workforce. Find the value of MP in the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form A P = Q" where A and n are positive constants. 3. The demand and total cost functions of a good are respectively 4P+Q-16=0 and ТС %3D 4 + 20 — 10 20 a) Find expressions for TR, (profit) 1 , MR, and MC in terms of Q. b) Solve the equation dn = 0 ÕP and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢'/, million per floor (e) Specialized costs of GH¢10000× per floor. How many floors should the office complex contain if…
- Q1) Deborah has 80 hours per week available for work and leisure. Her current rate is $25 per hour. Deborah has $400 of rental income every week. a) Construct a proper diagram to describe Deborah's choice of working 40 hours per week. Calculate Deborah's maximum possible income and optimal income, and show them in the diagram. b) Suppose Deborah recently moved into her boyfriend's place. She shares the household expenses and is "taxed" 50% of her wage income. Draw another diagram to compare Deborah's choice in Part a) and a new labor supply decision of working 50 hours per week due to the "tax". Clearly label out the income effect, substitution effect and total effect in the diagram.Deborah has 80 hours per week available for work and leisure. Her current wage rate is $25 per hour. Deborah has $400 of rental income every week. a) Construct a proper diagram to describe Deborah’s choice of working 40 hours per week. Calculate Deborah’s maximum possible income and optimal income, and show them in the diagram. b) Suppose Deborah recently moved into her boyfriend’s place. She shares the household expenses and is “taxed” 50% of her wage income. Draw another diagram to compare Deborah’s choice in Part a) and a new labor supply decision of working 50 hours per week due to the “tax”. Clearly label out the income effect, substitution effect and total effect in the diagram. Question Two Samantha has an annual non-labour income of $5000. Suppose she has the total available time of 4160 hours per year. Samantha's wage rate is $15 per hour, and she chooses to work 2000 hours in a year. Suppose when Samantha's wage rate increases from $15 to $18 per hour, she will work 2040…Sharon spends her time (16h) between leisure (L) and work and he consume Y product from his working income (P=1). Assume that she gets W$ per hour of working (W>0) and has the following utility function: U (L, Y) =LY 4Y. a.Calculate the demand function for L. and show it on a graph (L. vs W). b. Calculate the labor supply (H) and show it on a graph (H vs W). c.What will happen to L. Y and H if the wage per hour (W) will decrease?