Question

There is a hypothetical country endowed with 1500 labor hours, which can be used to producegoodsXandY. Assume that it takes 3 hours to produce one unit of goodXand 5 hours toproduce one unit of goodY.1. Equation _____ can be used to represent this country’s production possibility frontier.

A)1500 = 3X+5Y

B)1500 =13X+15Y

C)1500 = 5X≠3Y

D)1500 = 5X+3Y

Answer 1

Answer: A) 1500 = 3X + 5Y

The country is endowed with 1500 labor hours. It takes 3 hours to produce one unit of good X and 5 hours to produce one unit of good Y.

If the country produces only good X, then the maximum unit of good X, it can produce = 1500 / 3 = 500 units

If the country produces only good Y, then the maximum unit of good Y, it can produce = 1500 / 5 = 300 units

The equation of a line can be written as,

Y = b + mX

Where, b = Vertical intercept of the Y axis.

m = Slope of the line

Now, in the above figure, we see the line,which is actually the country’s production possibility frontier(PPF) passes through points, 500,0) and (0,300)

So, the slope of the above line will be,

m = ( 300 - 0) / ( 0 - 500)

Or, m = 300 / ( - 500)

Or, m = - 3 / 5

Let us now write the equation of the above line,

Y = 300 + ( - 3 / 5) X

Or, Y = (1500 - 3X) / 5

Or, 5Y = 1500 - 3X

Or, - 1500 = - 3X - 5Y

Or, 1500 = 3X + 5Y

So, equation ' 1500 = 3X + 5Y' can be used to represent this country’s production possibility frontier.

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