James has 16 hours of labour to allocate between producing goods X and Y which means...

James has 16 hours of labour to allocate between producing goods X and Y which means that LX + LY = 16. He also has 4 units of capital to allocate KX + KY = 4. Production functions are X = 2KX1/4LX1/4 and Y = KY1/4LY1/4. His tastes for the two activities are symmetric U = XY. a. Derive James’ Production Possibilities Frontier. Put Y on the vertical axis. Provide a labelled PPF graph showing the combination of Y and X that is consistent with his tastes. Making reference to your diagram, define “consistency” in this context. b. James should allocate _____________ units of labour and ____________ units of capital to the production of Good X.

Expert Solution

A production possibility frontier (PPF) shows the maximum possible output combinations of two goods or services an economy can achieve when all resources are fully and efficiently employed. Reallocating scarce resources from one product to another involves an opportunity cost. PPF is used to illustrate the trade-offs that arise from scarcity.

Assuming the tastes for two activities are symmetric.

Solving production funcitons of X & Y as follows:

K [X +Y] = 4

So, X +Y = 4/K

Similarly, X+Y = 16/L

therefore, 4/K = 16/L, i.e. 4K = L

K/L = 1/4 i.e. K = 1 units, L = 4 units

that means James should allocate 4 units of labour and 1 unit of capital to the production of good X.

All the points on PPF shows the consistency in his tastes like Point A on PPF that is optimum combination of factors of production i.e. Labour & Capital to production of the good X.

Rahul Sunny answered 2 years ago

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James has 16 hours of labour to allocate between producing goods X and Y which means...

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