Answer to Question #214605 in Macroeconomics for Jon

Question

Draw the Edgeworth box diagram for cocoa and coffee.
Label the point where both commodities cross each as R
Starting at the point where X1 crosses Y1, show that the output of cocoa, coffee, or both can be increased with the given amounts of 18L and 12K.
Derive the contract curve and indicate what it means.
What is the equilibrium condition that holds along the production contract curve and express it in an algebraic form?
What is the value of the MRTSLK?

Answer 1

(a)

Following below is the graphical presentation of the Edgeworth box diagram for cocoa and coffee:

(b)

Below mentioned is the well-labeled Edgeworth box diagram:

(c)

The X1 crosses Y1, at point R thus in order to increase the output of cocoa, coffee, or both the given amounts of 18L and 12K needs to be increased. Because the marginal rate of technical substitution depicts the rate of decrease in one factor in order to maintain the same level of productivity when another factor is increased.

$Since\space MRTSKL = dK/dL$

 Thus in order to increase the output for both the goods both the factors need to be increased.

d)

The contract curve is the locus of the point having pareto efficiency, ie where the indifference curve of Fred and Ginger are tangent. When the indifference curve are tangent the point is of pareto efficient, as no one can benefit by increasing their utility without making the other worse off. Here the curve will un fromero of coffee to zero cocoa.

e)

$\frac{Px}{Py}=\frac{MUx}{MUy}=\frac{y}{x}$

f)$MRTSLK = dL/dK$