Assume the hedonic wage function can be described as follow: H(r) = 2*(r-0.1), w

Question

Assume the hedonic wage function can be described as follow: H(r) = 2*(r-0.1), where r is the risk of getting injured such that r belong to the closed interval [0, 1]. That is, the probability of getting injured in larger or equal to zero and smaller or equal to 1 [i.e. 100%). Also, H(r) (which is larger or equal to zero] gives you the equilibrium wage that will be given by the labor market according to the level of risk offered by the firm.1T First, estate the hedonic wage function definition [you can find it in your course book) What is the interpretation of the slope? (5 points) Consider worker A values his wage and the safety (which is equal to 1 minus risk) level according to the following utility function: U (w, r) = w*(safty). What is the optimal amount of wage and risk this work is going to get? Assume there's a worker B willing to work in a riskier job than worker A. Show graphically (don't need to use specific numbers) the hedonic function, the indifferences curves of worker A and B and the intersection between these indifference curves and the Isoprofit of the firms C and D where worker A and B will choose to work, respectively. Suppose one of the firms represents a chemistry company and the other one a software company (as discussed in class). Which worker (A or B) will work in the chemistry company? Why? Discuss this allocation using the concept of matching in the work place.

Explanation / Answer

(a) Ginni coefficient is a measure of income inequality which is derived from lorenz curve. Ginni coefficient considers not just the income or GDP per capita, rather it takes into account cumulative income and cumulative population. Per capita GDP is an average measure which does not take into account the distribution of income within the country. So, the standard of living can not be judged only by looking at per capita GDP. Y can be argued as a better place to live because distribution of income may be more equal in the country with low ginni coefficient.

(b) The function given in the question explains the distribution of income as a function of accumulated percentage of population. By looking at this function, we cannot say that income is equally distributed, because a third of population is not receiving any income.

(c) Lorenz curve is constructed by taking cumulative population on the x-axis and cumulative income on the y-axis. The line of equality is a straight 45° line which represents equal distribution of income i.e. no inequality. The lower the lorenz curve from the equality line, higher the level of inequality in the economy.

The Gini coefficient is also a measure of inequality in distribution. Its value ranges between 0 and 1. It is calculated by taking the ratio of the area between the Lorenz curve of the distribution and the equal distribution line; with the area under the equal distribution line (the area of right triangle). As the denominator is 0.5, Gini index is equal to 1- 2B

Where B =  Integrand of lorenz curve function calculated for values between 0 and 1.

(d) When the total income is $2100, and the society has to be made egalitarian i.e. gini index zero, the the government should use the policy of taxing the rich to supplement the incomes of the poor, so that the cumulative share of population is always equal to the cumulative share of income.

(e) High skilled and low skilled labour differs in terms of its productivity. The wages that are paid to the labour are based on their productivity, thus skilled labour gets more wages as compared to unskilled labour and this discrimination creates a wedge between the workers and raises income inequality in US.

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