Question

An economy's production possibility boundary is given by the mathematical expression 20 = 4 A + B, where A is the quantity of good "a" and B is the quantity of good "b". [Hint: To help you answer this question, use the formula Y = mX + b and have good "a" quantities correspond to X-axis values and good "b" quantities correspond to Y-axis values.]

Part 1: If all the resources in the economy are allocated to producing good "a", what is the maximum level of production for this good ____________

Part 2: What is the maximum level of production for good "b" ____________

Part 3: What is the opportunity cost per unit of increasing the production of good “b” ____________

Part 4: Can the combination of 10 units of good A and 4 units of good B be produced in this economy (yes=1, no=2) ____________

Part 5: Can the combination of 22 units of good A and 18 units of good B be produced in this economy (yes=1, no=2) ____________

Answer 1

Production Possibility Boundary is given by-

4A + B = 20, where A is the quantity for good a and B is the quantity of good b.

Part 1) if all resources in the economy are allocated in the production of 'a', then production of 'b' becomes zero,i.e, B = 0

Thus, 4A + 0 = 20

or, A = 20/4 = 5.

The maximum level of production of good a is 5.

Part 2) the maximum level of production of good 'b' can happen when all the resources in the economy are allocated in the production of 'b', i.e, A= 0

4x0 + B = 20

or, B = 20

The maximum level of production of good 'b' is 20.

Part 3) Opportunity cost per unit of increasing the production of 'b' = 4/20 = 1/5

Part 4) 4A + B should be less than or equal to 20 for the given combination to be possible in the economy

But, 4x10+ 4 = 44>20, so NO.

Part 5) Again, 4x22+18 = 106>20, so NO