The economy – food F and light bulbs B

#2 There are two goods in the economy – food F and light bulbs B (used for the1 2 1 2 street light). Samantha’s utility is given by U 4F 2B , her income is $60 and prices are PF 1and PB 1.(a) How much of each good will she consume if she has to purchase everything byherself? What is her utility level?(b) How much of each good will she purchase herself, if her neighbour provides B 10 andshe can consume her neighbour’s street light without paying for it? What is her utilitylevel?(c) What is the minimum quantity of bulbs her neighbour needs to provide, for Samantha tooptimally choose to fully free-rider on her neighbour’s street light (i.e., not to purchaseany additional bulbs herself)? How much F will she consume? What is her utility level?(d) What hat happens to the quantities of F and B Samantha purchases herself if the neighbourprovides B* Bmin calculated in (c)? What total quantity of B will be consumed? Why? Showher new utility maximizing consumption point on the graph.#3. (21 marks) There are 2 sectors in the economy – food (F) and manufacturing (M). Assumethat VMPF 100 3LF and VMPM 220 LM and the total number of workers in theeconomy is 200.(a) Use the model of differential taxation of inputs to calculate the equilibrium split ofworkers between the industries and their wage.(b) If the government decides to provide a $120 per worker subsidy in F sector, use thesame model to calculate the new equilibrium split of workers and new wage. Showthe welfare change on the graph and calculate its net value. The subsidy is known tobe distortive and to generate a welfare loss, yet in this model it is associated with thewelfare gain. Briefly explain why.(c) If instead the government provides a $120 per worker subsidy in F sector and at the sametime imposes a $20 tax per worker in M sector, calculate the new equilibrium split ofworkers and new wage. Show the welfare change on the graph and calculate its net value.(d) Given your results in (c), would you advise the government that wants to expand thefood industry with the minimum change in wage to use the same size per workersubsidy or per worker tax? Briefly explain why.