According to the theory of income distribution that we learned in class, a worker's real wage reflects her productivity. Let's use this insight to examine the incomes of two groups of workers: farmers and barbers. Let Wf and Wb be the nominal wages of farmers and barbers, Pfand Pb be the prices of food and haircuts, and Af and Ab be the marginal productivity of farmers and barbers.

1. For each of the six variables defined above, state as precisely as you can the units in which they are measured. (Hint: Each answer takes the form "X per unit of Y.")
2. Over the past century, the productivity of farmers Af has risen substantially because of technological progress. According to the neoclassical theory that we learned in class, what should have happened to farmers' real wage, Wf/Pf ? In what units is this real wage measured?
3. Over the same period, the productivity of barbers Ab has remained constant. What should have happened to barbers' real wage, Wb / Pb ? In what units is this real wage measured?
4. Suppose that, in the long run, workers can move freely between being farmers and being barbers. What does this mobility imply for the nominal wages of farmers and barbers, Wf and Wb ? Why?
5. What do the previous answers imply for the price of haircuts relative to the price of food, Pb / P f ?
6. Suppose that barbers and farmers consume the same basket of goods and services. Who benefits more from technological progress in farming—farmers or barbers? Explain how your answer is consistent with the results on real wages in parts (b) and (c).

Answer:

a) The nominal wages Wf and Wb is measured in terms of money units per unit worker (either farmer or barber). Prices Pf and Pb are measured in terms of money units per unit output. The marginal productivity of the farmers and barbers Af and Ab respectively is measured in terms of output per worker. Distribution theory, in economics, the systematic attempt to account for the sharing of the national income among the owners of the factors of production—land, labour, and capital.

X=W_f+W_b Y= P_f+P_b

b) According to neoclassical theory wages are determined with respect to productivity which implies that higher productivity leads to higher wagers and lower productivity yields lower wages so as productivity of the farmers Af rises due to technological progress, the farmers' real wage (Wf/Pf) will also rise. The real wage for farmers (Wf/Pf) is measured as units of farm output per farmer.

c) If the marginal productivity of barbers is unchanged, then their real wage is unchanged. The real wage is measured in terms of haircuts. That is, if the nominal wage is in dollars, then the real wage is WH/PH, where PH is the dollar price of a haircut. Following neoclassical theory as marginal productivity of the barber Ab remains constant so the barbers' real wage (Wb/Pb) also remains unchanged that is constant. The real wage for barbers (Wb/Pb) is measured as units of barbers' output per barber.

d) In the long run since mobility of workers is present so as the real wage of farmers is more than that of barbers so workers shift to being farmers from barbers. So as the supply of farmers rise the marginal productivity per unit farmer falls so the nominal wage of farmers (Wf) falls and the nominal wage of barbers (Wb) rise as the supply of barbers fall which causes an increase in the marginal productivity per unit barber

e) If the nominal wage W is the same in both sectors, but the real wage in terms of farm goods is greater than the real wage in terms of haircuts, then the price of haircuts must have risen relative to the price of farm goods.

f) If both farmer and barber consume same basket of goods and services farmers will be benefitted more from this as with the increase in technology there's a subsequent decrease in cost and increase in profit thereby increasing his real wage and purchasing power. Barbers too will be benefitted as the food prices will fall thereby increasing their real purchasing power to buy other goods and services with the money saved from fall in food prices.