Question

about the question(ii) how to explain question(ii) G/F=F=8 and G=F^2=8

ii. If trade is possible, what is the optimum production and consumption bundle if the relative price between fish and grain is 8? (i.e. Price of fish is 8 and price of grain is 1.)

b. Suppose a simple economy produces only fish (F) and grain (G). The production possibility frontier for fish and grain is given by f/2g-337.5. Assuming G is plotted on the vertical axis and F is plotted on the horizontal axis, the marginal rate of substitution and the marginal rate of transformation between fish and grain are G/F and F respectively i.What is the optimum production and consumption bundle without trade? (6 marks) ii. If trade is possible, what is the optimum production and consumption bundle if the relative price between fish and grain is 8? (i.e. Price of fish is 8 and price of grain is 1.) (6 marks) part ä s prefered to iii. show the optimum that obtained from part ii is preferred to the one obtained from part 1. (3 marks) 61 2- -t 333 5 333 S

Answer 1

A) putting mrs=mrt

G=f^2 in ppf equation

F=15, g=225

B) putting mrs=mre

G=8f in ppf equation

F^2/2 + 8f=337.5

F^2+16f- 675=0

Solving this yields f*= 19.1845 and g*=153.476

We can check that f* and g* satisfy ppf equation. Hence it is a feasible bundle.

C) optimum obtained from (ii) is better than (i) because in first part 225/15 =15 >8. Hence the budget line should be more steeper to make (i) bundle optimum after trade. Hence when price ratio is 8, (i) bundle lies below the budget line and not an optimum one.