Reference no: EM133770768

Assignment: Macro Economics with Graph

Department of Economics

I. Avery has preferences over gum (?1) and lollipops (?2) with her utility function given by ?(?1, ?2) = 0.25 ln ?1 + 0.75 ln ?2. Further, the price of gum is given by p1 and the price of lollipops is given by p2 and income is denoted by y.

i. Suppose that given utility and prices, Avery gum and lollipops in such a way that ?1=2.5 and ?2=1 when income is 8. How many lollipops (?2) is Avery willing to give up to get an extra unit of gum (?2)?
ii. If p1 = 2 and p2 = 3, is the choice from a) affordable? How many lollipops does Avery have to give up to get an extra unit of gum?

iii. With the aid of a diagram, explain why this choice is not optimal. Should Avery consume more gum?

iv. What is Avery's optimal choice of gum and lollipops in terms of p1, p2, and y? What are these choices when p1 = 2, p2 = 3, and y = 8?

v. If Avery's income falls to y = 4, how is consumption of both goods affected? Illustrate graphically. Are gum and lollipops "normal" goods?

II. Carolina values consumption (iii) and leisure (?). She has 16 units of time to divide between working or enjoying leisure. For each hour worked she receives 10 units of the consumption good. Suppose that Carolina's preferences are such that, she is willing to give up 2?/? units of consumption for an additional unit of leisure. Carolina also owns shares in a factory which gives dividend income of 16. The government in this economy taxes labour income only at a rate of 20% (i.e. T=0).

i. Write down the budget constraint Carolina faces. Explain how she should determine consumption and leisure in order to maximize utility.

ii. Find the optimal choice of consumption and leisure and illustrate graphically. Explain why 6 units of labour is not an optimal choice.c) If everyone else in this economy has the same income and same preferences, and the total population is 50 people (including Carolina). What is GDP using the income approach and expenditure approach.

iii. If the government would like to increase government spending by raising the tax rate to 40%, how does this affect the optimal choice of consumption and leisure? Do you think GDP will rise or fall?

iv. Explain your result in d) in terms of income and substitution effects. Illustrate graphically. Which effect is the strongest in this case?

III. Magna is a firm that employs capital K and labour N to produce automobile parts. Its production function is given by ? = ?(?, ?) = ????1?? in which z is total factor productivity. Assume that z = 100, K = 1, ? = 0.5 and each worker supplies one unit of labour paid at the wage rate w. Further, output is sold for P = 1 and the wage rate is 6.25 in the labour market.

i. When Magna hires 16 workers, each worker produces 25 goods on average (average product is 25). If they hire 9 more workers, then average product falls to 20. Has Magna hired lazy workers? How Magna can make each worker more productive.

ii. If Magna hires 100 workers (i.e. to set N = 100). Is this a good decision? How many workers should Magna hire (optimal labour selection)?

iii. The government decides to prevent any firm from polluting. Magna discovers that polluting can be avoided at the cost of 0.25 units of output per unit of output produced. How many workers will Magna hire if w = 6.25?

iv. If the government decides to subsidize Magna (to alleviate the cost of pollution reduction) by 1.25 per worker hired. How many workers will Magna hire if the wage rate is unchanged?

v. How will the policies introduced in (iii) and in (iv) affect the firms inverse labour demand curve? How will the equilibrium wage be affected if all firms in the economy are identical to Magna's firm? Illustrate graphically.