Consider a variation of the model of Veblen effects, conspicuous consumption, and working time, presented in Bowles and Halliday, Suppose now that the consumer has preferences over consumption, x, and labour, 0 0 denotes the Veblen effect and x denotes the consumption of the rich, so that effective consumption may be written x = x vx. a) [5 marks] Write down the consumer's budget constraint, and sketch it, along with the feasible budget set, in the xh-space. b) [5 marks] Find an expression for a consumer's indifference curve, and characterize its slope, intercepts (if any), and curvature. Then, sketch a few such curves in the xh-space, together with the constraint found in a). Where would the optimum lie? Explain your answer. c) [10 marks] Solve the consumer's optimization problem for x and h. Do the original model's conclusions regarding the link between income inequality and work hours still hold? Why or why not? Explain your answer. d) [10 marks] Suppose instead that u(x, h) = x-vx-(1/2) h. Is income inequality still a concern for work hours in this case? Is conspicuous consumption of the rich still a public bad"? Explain your answers.