Question

A certain economy produces only two goods: beer (B) and whiskey (W). The only scarce resource is labour. There are 1,000 labour hours available in this economy. One labour hour produces either 100 litres of beer or 50 litres of whiskey. Some citizens supply lots of labour hours, some few. The citizens of this economy all have utility functions of the form U(B, W) = B1/2W1/2 . State if the following statement is true, false, or uncertain. Explain your answer and support it by a graph.

(a) At every Pareto efficient allocation, the number of litres of beer produced equals the number of litres of whiskey produced.

(b) At every Pareto efficient allocation, total beer production is 500,000 litres.

(c) At every Pareto efficient allocation, all citizens consume the same commodity bundle.

(d) At every Pareto efficient allocation, every consumer?s marginal rate of substitution between beer and whiskey is -1/2.

(e) Repeat parts a) to d) for the utility function U(B, W) = B + 2W.

(f) Repeat parts a) to d) for the utility function U(B, W) = min{B, 2W}.

Answer 1

Consider the given problem here there are two goods “B=beer” and “W=whiskey”. Now, the input requirement for both the goods are given, => the PPF of this economy is given by.

=> B/100 + W/50 = 1000. Now, because labor is the only input, => as we withdraw some labor from one sector and employ it into another sector, => the production of one sector decreases and the production of another sector decreases. So, here alone the PPF all production points are Pareto efficient.

a).

Consider the following fig.

So, here all the points on the PPF are Pareto efficient. SO, here if we move from “A1” to “A2” alone the PPF then the production of “B” increase and “W” decreases, => production of “B” and “W” can’t be equal, => the given statement is “FALSE”.

b).

Now, in the above fig “A2” be the production point where the economy is producing “B=100,000 unit” and “W=0 units”. Now, as we move alone the PPF towards the left the production of “B” decreases and “W” increases, => production of “B” can’t fixed at “500,000”, => “FALSE”.

c).

Now, here all the citizen having same types of preference, => their option choice will be same given the market price of both the goods. TRUE.

d).

Now, the utility function is given by, “U=B^0.5*W^0.5”, => MUB = 0.5*(W/B)^0.5 and MUW = 0.5*(B/W)^0.5. => MRS = W/B = not constant. So, at all the pareto efficient point the MRS is not constant, => FALSE.